A325121 Sum of binary digits of the prime indices of n.

0, 1, 1, 2, 2, 2, 1, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 1, 4, 2, 3, 2, 4, 4, 3, 3, 3, 2, 4, 3, 5, 3, 4, 3, 4, 2, 2, 3, 5, 3, 3, 3, 4, 4, 3, 4, 5, 2, 5, 4, 4, 1, 4, 4, 4, 2, 3, 2, 5, 2, 4, 3, 6, 4, 4, 3, 5, 3, 4, 2, 5, 3, 3, 5, 3, 3, 4, 3, 6, 4, 4, 4, 4, 5, 4, 3

Offset

1,4

Comments

The sum of binary digits of an integer is the number of 1's in its binary representation. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Totally additive with a(prime(n)) = A000120(n).

Mathematica

Table[Sum[pr[[2]]*DigitCount[PrimePi[pr[[1]]], 2, 1], {pr, FactorInteger[n]}], {n, 100}]

Prog

(PARI) a(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2] * hammingweight(primepi(f[i, 1]))); } \\ Amiram Eldar, Jan 17 2026

Crossrefs

Cf. A000120, A000720, A001222, A019565, A048881, A070939, A112798.

Cf. A325103, A325104, A325106, A325118, A325119.

Other totally additive sequences: A056239, A302242, A318994, A318995, A325033, A325034, A325120, A325122.

Sequence in context: A316506 A294884 A275024 * A064659 A349520 A325034

Adjacent sequences: A325118 A325119 A325120 * A325122 A325123 A325124

Keyword

nonn,easy,base

Author

Gus Wiseman, Mar 29 2019

Status

approved