A388976 a(n) = A033885(n) * A003961(n), where A033885(n) = 3*n-sigma(n), and A003961 is fully multiplicative with a(p) = nextprime(p).

2, 9, 25, 45, 63, 90, 143, 243, 350, 252, 273, 360, 425, 594, 735, 1377, 627, 1125, 851, 1134, 1705, 1170, 1305, 1620, 2156, 1836, 5125, 2772, 1767, 1890, 2257, 8019, 3315, 2736, 4389, 3825, 2993, 3726, 5185, 5670, 3483, 4950, 3995, 5616, 9975, 5742, 4929, 8100, 10890, 8379, 7695, 8874, 6195, 15750, 8463, 14256

Offset

1,1

Comments

The first negative term is a(180) = -9450.

Links

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

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

Formula

a(n) = 3*A191002(n) - A341529(n) = (n*A003961(2*n)) - A341529(n).

a(n) <= A388977(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A033885(n) = (3*n-sigma(n));
A388976(n) = (A033885(n)*A003961(n));

Crossrefs

Cf. A000203, A003961, A005820 (positions of 0's), A033885, A191002, A249734, A341529, A388977.

Sequence in context: A360515 A226388 A053194 * A346069 A005582 A173965

Adjacent sequences: A388973 A388974 A388975 * A388977 A388978 A388979

Keyword

sign,easy

Author

Antti Karttunen, Sep 22 2025

Status

approved