A365454 a(n) = gcd(sigma(n), A156552(2*n)).

1, 3, 1, 7, 3, 1, 1, 15, 13, 1, 3, 1, 1, 1, 3, 31, 3, 3, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 1, 63, 3, 1, 1, 1, 1, 5, 7, 1, 3, 3, 1, 3, 3, 1, 3, 1, 1, 3, 9, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 127, 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 1, 1, 3, 3, 5, 3, 1, 7, 3, 1, 1, 1, 1, 1, 1, 13, 1, 3, 1, 1, 1, 1, 1, 9, 3, 1, 1, 1, 1, 1, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = gcd(A000203(n), A156552(2*n)).

a(n) = A000203(n) / A365455(n) = A156552(2*n) / A365456(n).

For all n >= 0, a(2^n) = 2^(1+n) - 1 = A000225(1+n).

Prog

(PARI)
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A365454(n) = gcd(sigma(n), A156552(2*n));

Crossrefs

Cf. A000203, A000225, A156552, A365455, A365456.

Sequence in context: A297156 A132885 A187818 * A059090 A327990 A133115

Adjacent sequences: A365451 A365452 A365453 * A365455 A365456 A365457

Keyword

nonn

Author

Antti Karttunen, Sep 10 2023

Status

approved