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A325036 Difference between product and sum of prime indices of n. 8
1, 0, 0, -1, 0, -1, 0, -2, 0, -1, 0, -2, 0, -1, 1, -3, 0, -1, 0, -2, 2, -1, 0, -3, 3, -1, 2, -2, 0, 0, 0, -4, 3, -1, 5, -2, 0, -1, 4, -3, 0, 1, 0, -2, 5, -1, 0, -4, 8, 2, 5, -2, 0, 1, 7, -3, 6, -1, 0, -1, 0, -1, 8, -5, 9, 2, 0, -2, 7, 4, 0, -3, 0, -1, 10, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

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..76.

FORMULA

a(n) = A003963(n) - A056239(n).

EXAMPLE

The prime indices of 45 are {2,2,3}, with product 12 and sum 7, so a(45) = 5.

MATHEMATICA

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

Table[Times@@primeMS[n]-Total[primeMS[n]], {n, 100}]

CROSSREFS

Positions of zeros are A301987. Positions of ones are A325041. Positions of negative ones are A325042.

Cf. A000720, A001222, A003963, A056239, A112798, A178503, A175508, A319000.

Cf. A325032, A325033, A325034, A325035, A325037, A325038, A325044.

Sequence in context: A039995 A035232 A091603 * A194942 A129688 A309011

Adjacent sequences:  A325033 A325034 A325035 * A325037 A325038 A325039

KEYWORD

sign

AUTHOR

Gus Wiseman, Mar 25 2019

STATUS

approved

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Last modified January 25 16:01 EST 2022. Contains 350572 sequences. (Running on oeis4.)