A359777 Numbers k such that A356163(k) = 1 but A359774(k) = 0, where A359774 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with an even sum of prime factors, with repetition).

4, 8, 16, 32, 36, 60, 64, 72, 81, 84, 100, 120, 128, 132, 140, 144, 156, 162, 168, 196, 200, 204, 220, 225, 228, 240, 256, 260, 264, 276, 280, 288, 308, 312, 324, 336, 340, 348, 364, 372, 380, 392, 400, 408, 440, 441, 444, 450, 456, 460, 476, 480, 484, 492, 512, 516, 520, 528, 532, 540, 552, 560, 564

Offset: 1

Author

Antti Karttunen, Jan 15 2023

Keywords

• nonn

Crossrefs

Cf. A001414, A356163, A359773, A359774.

Setwise difference A036349 \ A359775.

Setwise difference A359776 \ A335657.

Cf. also A359767, A359784.

Programs

PARI

A356163(n) = (1-(((n=factor(n))[, 1]~*n[, 2])%2)); \\ After code in A001414.
memoA359773 = Map();
A359773(n) = if(1==n,1,my(v); if(mapisdefined(memoA359773,n,&v), v, v = -sumdiv(n,d,if(dA356163(n/d)*A359773(d),0)); mapput(memoA359773,n,v); (v)));
A359774(n) = (A359773(n)%2);
isA359767(n) = (A356163(n)&&!(A359774(n)));

Formula

{k | A356163(k)-A359774(k) == 1}.