A325032 Product of products of the multisets of prime indices of each prime index of n.

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

Offset

1,5

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

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

Fully multiplicative with a(prime(n)) = A003963(n).

Example

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

Mathematica

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

Prog

(PARI) \\ here b(n) is A003963(n).
b(n) = { my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); primepi(p)^e) }
a(n) = { my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); b(primepi(p))^e) } \\ Andrew Howroyd, Nov 10 2025

Crossrefs

Cf. A000720, A001055, A001222, A003963, A056239, A112798, A302242, A320325.

Cf. A324850, A324926, A324930, A325031, A325033, A325034, A325035.

Sequence in context: A083671 A201913 A232463 * A270000 A029384 A225485

Adjacent sequences: A325029 A325030 A325031 * A325033 A325034 A325035

Keyword

nonn,mult

Author

Gus Wiseman, Mar 25 2019

Status

approved