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

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: A027640 A349448 A194666 * A355930 A229946 A127460

Adjacent sequences: A325796 A325797 A325798 * A325800 A325801 A325802

Keyword

nonn

Author

Gus Wiseman, May 23 2019

Status

approved