A368910 Partial sums of A368909.

0, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Formula

a(0) = 0, and for n > 0, a(n) = a(n-1) + A368909(n), where A368909(n) = A003415(sigma(A005940(1+n))) mod 2.

Prog

(PARI)
up_to = 65537;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A368909(n) = (A003415(sigma(A005940(1+n)))%2);
A368910list(up_to) = { my(v=vector(up_to), s=A368909(0)); for(i=1, up_to, s +=
A368909(i); v[i] = s); (v); };
v368910 = A368910list(up_to);
A368910(n) = if(!n, A368909(0), v368910[n]);

Crossrefs

Partial sums of A368909.

Cf. A000203, A003415, A005940, A165560, A324054, A347870.

Cf. also A349909.

Sequence in context: A216256 A309407 A046693 * A196376 A156077 A189641

Adjacent sequences: A368907 A368908 A368909 * A368911 A368912 A368913

Keyword

nonn

Author

Antti Karttunen, Jan 11 2024

Status

approved