The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Daniel Suteu (See also Daniel Suteu's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A377634

a(n) is the smallest k such that tau(k*2^n - 1) is equal to 2^n where tau = A000005.
(history; published version)

#21 by Daniel Suteu at Tue Jan 07 10:21:00 EST 2025

STATUS

editing

proposed

#20 by Daniel Suteu at Tue Jan 07 10:17:55 EST 2025

DATA

2, 4, 17, 130, 1283, 6889, 40037, 638521, 10126943, 186814849, 2092495862

COMMENTS

a(12) <= 8167862431, a(13) <= 1052676193433, a(14) <= 30964627320559. - Daniel Suteu, Jan 07 2025

FORMULA

a(n)*2^n - 1 >= A360438(n). - Daniel Suteu, Jan 07 2025

CROSSREFS

Cf. A000005, A360438.

EXTENSIONS

a(11) from Daniel Suteu, Jan 07 2025

STATUS

approved

editing

A118883

Smallest prime p with bigomega(p+1)=n, where bigomega(m)=A001222(m) is the number of prime divisors of m (counted with multiplicity).
(history; published version)

#15 by Daniel Suteu at Tue Jan 07 02:43:10 EST 2025

STATUS

editing

proposed

#14 by Daniel Suteu at Tue Jan 07 02:42:22 EST 2025

PROG

(PARI)

almost_primes(A, B, n) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p, ceil(A/m)), B\m, listput(list, m*q)), forprime(q=p, sqrtnint(B\m, n), list=concat(list, f(m*q, q, n-1)))); list); vecsort(Vec(f(1, 2, n)));

a(n) = my(x=2^n, y=2*x); while(1, my(v=almost_primes(x, y, n)); for(k=1, #v, if(isprime(v[k]-1), return(v[k]-1))); x=y+1; y=2*x); \\ Daniel Suteu, Jan 07 2025

STATUS

approved

editing

A073919

Smallest prime p with bigomega(p-1)=n, where bigomega(m)=A001222(m) is the number of prime divisors of m (counted with multiplicity).
(history; published version)

#24 by Daniel Suteu at Tue Jan 07 02:38:57 EST 2025

STATUS

editing

proposed

#23 by Daniel Suteu at Tue Jan 07 02:37:14 EST 2025

PROG

(PARI)

a(n) = if(n==0, return(2)); my(x=2^n, y=2*x); while(1, my(v=almost_primes(x, y, n)); for(k=1, #v, if(isprime(v[k]+1), return(v[k]+1))); x=y+1; y=2*x); \\ Daniel Suteu, Jan 07 2025

STATUS

approved

editing

A379768

a(n) is the smallest prime p such that omega(p^n + 1) = n.
(history; published version)

#12 by Daniel Suteu at Mon Jan 06 09:36:36 EST 2025

STATUS

editing

proposed

#11 by Daniel Suteu at Mon Jan 06 09:33:21 EST 2025

COMMENTS

2 * 10^6 < a(16) <= 206874667; a(18) = 33577; a(20) <= 3258569.

EXAMPLE

a(3) = 5 is the smallest prime number of the set {p(i)} = {5, 11, 13, 19, 23, ...} where omega(p(i)^3 + 1) = 3.

MATHEMATICA

a[n_] := Module[{p = 2}, While[PrimeNu[p^n + 1] != n, p = NextPrime[p]]; p]; Print[Array[a, 11]]

#10 by Daniel Suteu at Mon Jan 06 07:33:41 EST 2025

NAME

allocated for Daniel Suteu

a(n) is the smallest prime p such that omega(p^n + 1) = n.

DATA

2, 3, 5, 43, 17, 47, 151, 1697, 59, 2153, 521, 13183, 30089, 66569, 761

OFFSET

1,1

COMMENTS

2 * 10^6 < a(16) <= 206874667; a(18) = 33577;

FORMULA

A219018(n) <= a(n) <= A280005(n).

EXAMPLE

a(3) = 5 is the smallest prime number of the set {p(i)} = {5, 11, 13, 19, 23, ...} where omega(p(i)^3 + 1) = 3.

PROG

(PARI) a(n) = forprime(p=2, oo, if(omega(p^n+1) == n, return(p)));

CROSSREFS

Cf. A001221, A219018, A242786, A280005, A362957, A379450.

KEYWORD

allocated

nonn,more,hard

AUTHOR

Daniel Suteu, Jan 06 2025

STATUS

approved

editing

#9 by Daniel Suteu at Mon Jan 06 07:33:41 EST 2025

NAME

allocated for Daniel Suteu

KEYWORD

recycled

allocated