A354997 a(n) = A351547(n) / A351546(n).

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 5, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 7, 1, 1, 1, 3, 1

Offset

1,8

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A351547(n) / A351546(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351546(n) = { my(f=factor(sigma(n)), u=A003961(n)); prod(k=1, #f~, f[k, 1]^((0!=(u%f[k, 1]))*f[k, 2])); };
A351547(n) = { my(s=sigma(n), f=factor(s), u=A003961(n)); s/prod(k=1, #f~, if(!(u%f[k, 1]) && (f[k, 2]>=valuation(u, f[k, 1])), f[k, 1]^f[k, 2], 1)); };
A354997(n) = (A351547(n) / A351546(n));

Crossrefs

Cf. A000203, A003961, A351545, A351546, A351547.

Sequence in context: A093818 A097031 A372565 * A327537 A120263 A250208

Adjacent sequences: A354994 A354995 A354996 * A354998 A354999 A355000

Keyword

nonn

Author

Antti Karttunen, Jul 09 2022

Status

approved