A325034 Sum of products of the multisets of prime indices of each prime index of n.

0, 1, 1, 2, 2, 2, 1, 3, 2, 3, 3, 3, 2, 2, 3, 4, 4, 3, 1, 4, 2, 4, 4, 4, 4, 3, 3, 3, 3, 4, 5, 5, 4, 5, 3, 4, 2, 2, 3, 5, 6, 3, 4, 5, 4, 5, 6, 5, 2, 5, 5, 4, 1, 4, 5, 4, 2, 4, 7, 5, 4, 6, 3, 6, 4, 5, 8, 6, 5, 4, 3, 5, 8, 3, 5, 3, 4, 4, 5, 6, 4, 7, 9, 4, 6, 5, 4

Offset

1,4

Comments

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)) = A003963(n).

Example

94 has prime indices {1,15} with prime indices {{},{2,3}} with products {1,6} with sum a(94) = 7.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Plus@@Times@@@primeMS/@primeMS[n], {n, 100}]

Prog

(PARI) A003963(n) = {my(f = factor(n)); prod(i = 1, #f~, primepi(f[i, 1])^f[i, 2]); }
a(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2] * A003963(primepi(f[i, 1]))); } \\ Amiram Eldar, Jan 17 2026

Crossrefs

Cf. A000720, A001055, A001222, A003963, A056239, A066739, A112798, A302242.

Cf. A324926, A325031, A325032, A325033, A325035.

Sequence in context: A325121 A064659 A349520 * A275853 A324100 A127953

Adjacent sequences: A325031 A325032 A325033 * A325035 A325036 A325037

Keyword

nonn,easy

Author

Gus Wiseman, Mar 25 2019

Status

approved