A366749 Self-signed alternating sum of the prime indices of n.

0, -1, 2, -2, -3, 1, 4, -3, 4, -4, -5, 0, 6, 3, -1, -4, -7, 3, 8, -5, 6, -6, -9, -1, -6, 5, 6, 2, 10, -2, -11, -5, -3, -8, 1, 2, 12, 7, 8, -6, -13, 5, 14, -7, 1, -10, -15, -2, 8, -7, -5, 4, 16, 5, -8, 1, 10, 9, -17, -3, 18, -12, 8, -6, 3, -4, -19, -9, -7, 0

Offset

1,3

Comments

We define the self-signed alternating sum of a multiset y to be Sum_{k in y} k*(-1)^k.

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..70.

Formula

a(n) = Sum_{k in A112798(n)} k*(-1)^k.

a(n) = A366531(n) - A366528(n).

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
asum[y_]:=Sum[x*(-1)^x, {x, y}];
Table[asum[prix[n]], {n, 100}]

Crossrefs

With summands of 2^(n-1) we get A048675.

With summands of (-1)^k we get A195017.

The version for alternating prime indices is A346697 - A346698 = A316524.

Positions of zeros are A366748, counted by A239261.

A112798 lists prime indices, length A001222, sum A056239, reverse A296150.

A300061 lists numbers with even sum of prime indices, odd A300063.

A366528 adds up odd prime indices, counted by A113685.

A366531 adds up even prime indices, counted by A113686.

Cf. A000720, A019507, A045931, A055396, A061395, A325698, A325700, A366533.

Sequence in context: A353931 A354871 A303777 * A304529 A071281 A361249

Adjacent sequences: A366746 A366747 A366748 * A366750 A366751 A366752

Keyword

sign

Author

Gus Wiseman, Oct 23 2023

Status

approved