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A325799 Sum of the prime indices of n minus the number of distinct positive subset-sums of the prime indices of n. 4
0, 0, 1, 0, 2, 0, 3, 0, 2, 1, 4, 0, 5, 2, 2, 0, 6, 0, 7, 0, 3, 3, 8, 0, 4, 4, 3, 1, 9, 0, 10, 0, 4, 5, 4, 0, 11, 6, 5, 0, 12, 0, 13, 2, 2, 7, 14, 0, 6, 2, 6, 3, 15, 0, 5, 0, 7, 8, 16, 0, 17, 9, 4, 0, 6, 1, 18, 4, 8, 2, 19, 0, 20, 10, 3, 5, 6, 2, 21, 0, 4, 11 (list; graph; refs; listen; history; text; internal format)
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, with sum A056239(n). A positive subset-sum of an integer partition is any sum of a nonempty submultiset of it.

LINKS

Table of n, a(n) for n=1..82.

FORMULA

a(n) = A056239(n) - A304793(n).

EXAMPLE

The prime indices of 21 are {2,4}, with positive subset-sums {2,4,6}, so a(21) = 6 - 3 = 3.

MATHEMATICA

hwt[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>PrimePi[p] k]];

Table[hwt[n]-Length[Union[hwt/@Rest[Divisors[n]]]], {n, 30}]

CROSSREFS

Positions of 1's are A325800.

Positions of nonzero terms are A325798.

Cf. A000005, A002033, A056239, A108917, A112798, A276024, A299702, A304793.

Cf. A325694, A325780, A325794, A325801, A325802.

Sequence in context: A292561 A027640 A194666 * A229946 A127460 A274021

Adjacent sequences:  A325796 A325797 A325798 * A325800 A325801 A325802

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 23 2019

STATUS

approved

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Last modified August 5 06:10 EDT 2021. Contains 346457 sequences. (Running on oeis4.)