A325799 - OEIS

A325799

Sum of the prime indices of n minus the number of distinct positive subset-sums of the prime indices of n.

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

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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.