A340071 - OEIS

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A340071

a(n) = gcd(A003961(n)-1, phi(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes.

6

1, 2, 4, 2, 6, 2, 10, 2, 4, 4, 12, 4, 16, 4, 2, 2, 18, 2, 22, 2, 2, 2, 28, 2, 6, 2, 4, 2, 30, 8, 36, 2, 16, 4, 4, 8, 40, 4, 4, 4, 42, 4, 46, 4, 6, 2, 52, 4, 10, 2, 2, 8, 58, 2, 18, 4, 2, 4, 60, 2, 66, 2, 2, 2, 2, 2, 70, 2, 16, 10, 72, 2, 78, 2, 4, 2, 2, 2, 82, 2, 4, 4, 88, 2, 12, 4, 2, 2, 96, 4, 2, 4, 8, 2, 4, 2, 100

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OFFSET

1,2

COMMENTS

Prime shifted analog of A049559.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = A049559(A003961(n)).

a(n) = gcd(A253885(n-1), A003972(n)) = gcd(A003961(n)-1, A000010(A003961(n))).

a(n) = A003972(n) / A340072(n).

For n > 1, a(n) = (A003961(n)-1) / A340073(n).

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A340071(n) = { my(u=A003961(n)); gcd(u-1, eulerphi(u)); };

CROSSREFS

Cf. A000010, A003961, A003972, A049559, A253885, A340072, A340073.

Cf. also A340081.

Sequence in context: A212122 A213372 A286601 * A102128 A181980 A230436

Adjacent sequences: A340068 A340069 A340070 * A340072 A340073 A340074

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 28 2020

STATUS

approved