A326135 a(n) = sigma(A028234(n)), where sigma is the sum of divisors of n, and A028234 gives n without any occurrence of its smallest prime factor.

1, 1, 1, 1, 1, 4, 1, 1, 1, 6, 1, 4, 1, 8, 6, 1, 1, 13, 1, 6, 8, 12, 1, 4, 1, 14, 1, 8, 1, 24, 1, 1, 12, 18, 8, 13, 1, 20, 14, 6, 1, 32, 1, 12, 6, 24, 1, 4, 1, 31, 18, 14, 1, 40, 12, 8, 20, 30, 1, 24, 1, 32, 8, 1, 14, 48, 1, 18, 24, 48, 1, 13, 1, 38, 31, 20, 12, 56, 1, 6, 1, 42, 1, 32, 18, 44, 30, 12, 1, 78, 14, 24, 32, 48, 20, 4, 1

Offset: 1

Author

Antti Karttunen, Jun 08 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A013661, A028234, A326065, A326136.

Programs

PARI

A028234(n) = { my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); }; \\ From A028234
A326135(n) = sigma(A028234(n));

Formula

a(n) = A000203(A028234(n)).

a(n) = A326065(n) / A000203(A020639(n)^(A067029(n)-1)).

Sum_{k=1..n} a(k) ~ (zeta(2)/2) * c * n^2, where c = Sum_{p prime} ((1/(p^2-1)) * Product_{prime q <= p} ((q-1)^2*(q+1)/q^3)) = 0.166218264542... . - Amiram Eldar, Dec 21 2024