A326136 a(n) = sigma(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.

0, 2, 3, 6, 5, 8, 7, 14, 12, 12, 11, 24, 13, 16, 18, 30, 17, 26, 19, 36, 24, 24, 23, 56, 30, 28, 39, 48, 29, 48, 31, 62, 36, 36, 40, 78, 37, 40, 42, 84, 41, 64, 43, 72, 72, 48, 47, 120, 56, 62, 54, 84, 53, 80, 60, 112, 60, 60, 59, 144, 61, 64, 96, 126, 70, 96, 67, 108, 72, 96, 71, 182, 73, 76, 93, 120, 84, 112, 79, 180, 120, 84, 83

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n).

Formula

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

From Amiram Eldar, Dec 21 2024: (Start)

a(n) = A000203(n) - A326135(n).

Sum_{k=1..n} a(k) ~ (zeta(2)/2) * (1 - c) * n^2, where c is defined in the corresponding formula in A326135. (End)

Prog

(PARI)
A028234(n) = { my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); }; \\ From A028234
A326136(n) = (sigma(n) - sigma(A028234(n)));

Crossrefs

Cf. A000203, A013661, A028234, A326066, A326135.

Sequence in context: A354629 A048750 A344403 * A276081 A329564 A257011

Adjacent sequences: A326133 A326134 A326135 * A326137 A326138 A326139

Keyword

nonn

Author

Antti Karttunen, Jun 08 2019

Status

approved