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A325034 Sum of products of the multisets of prime indices of each prime index of n. 7
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..87.

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}]

CROSSREFS

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

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

Sequence in context: A275024 A325121 A064659 * A275853 A324100 A127953

Adjacent sequences:  A325031 A325032 A325033 * A325035 A325036 A325037

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 25 2019

STATUS

approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)