

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
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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



