A360355 - OEIS

A360355

Primitive terms of A360328: terms of A360328 with no proper divisor in A360328.

7425, 8415, 46035, 76725, 101475, 182655, 355725, 669735, 1411425, 1606275, 2352375, 2891295, 3592215, 3650625, 4079295, 4861575, 5053455, 5870205, 6093225, 6636465, 6920595, 7732395, 8750835, 9120375, 9783675, 9850005, 9958905, 10155375, 11298375, 11532375, 12120075

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OFFSET

1,1

COMMENTS

If m is a term then k*m is a term of A360328 for all k in A076610.

Analogous to primitive abundant numbers (A091191) with divisors that are restricted to numbers that have only prime-indexed prime factors.

LINKS

Table of n, a(n) for n=1..31.

MATHEMATICA

f[p_, e_] := If[PrimeQ[PrimePi[p]], (p^(e + 1) - 1)/(p - 1), 1]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; primQ[n_] := s[n] > 2*n && AllTrue[Divisors[n], # == n || s[#] <= 2*# &]; Select[Range[10^6], primQ]

PROG

(PARI) isab(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(isprime(primepi(p[i])), (p[i]^(e[i]+1)-1)/(p[i]-1), 1)) > 2*n; }

is(n) = {if(!isab(n), return(0)); fordiv(n, d, if(d < n && isab(d), return(0))); return(1)};

CROSSREFS

Subsequence of A360328.

Cf. A076610.

Similar sequences: A006038, A091191, A249263, A302574, A360356.

Sequence in context: A116195 A249878 A360328 * A324897 A051259 A289517

Adjacent sequences: A360352 A360353 A360354 * A360356 A360357 A360358

KEYWORD

nonn

AUTHOR

Amiram Eldar, Feb 04 2023

STATUS

approved