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

1,1

Links

Table of n, a(n) for n=1..63.

Formula

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

Prog

(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(d<n, A356163(n/d)*A359773(d), 0)); mapput(memoA359773, n, v); (v)));
A359774(n) = (A359773(n)%2);
isA359767(n) = (A356163(n)&&!(A359774(n)));

Crossrefs

Cf. A001414, A356163, A359773, A359774.

Setwise difference A036349 \ A359775.

Setwise difference A359776 \ A335657.

Cf. also A359767, A359784.

Sequence in context: A125626 A141031 A061011 * A181800 A319180 A075090

Adjacent sequences: A359774 A359775 A359776 * A359778 A359779 A359780

Keyword

nonn

Author

Antti Karttunen, Jan 15 2023

Status

approved