A374210 Partial sums of A059339.

0, 0, 1, 2, 2, 3, 3, 4, 5, 8, 8, 10, 10, 12, 14, 15, 15, 16, 16, 18, 19, 23, 23, 25, 26, 30, 35, 41, 41, 42, 42, 44, 45, 50, 51, 54, 54, 56, 58, 62, 62, 65, 65, 70, 77, 81, 81, 84, 85, 89, 89, 96, 96, 99, 100, 105, 105, 110, 110, 116, 116, 119, 126, 130, 130, 134, 134, 144, 145, 151, 151, 155, 155, 160, 168, 178

Offset

1,4

Comments

Though the data for the early growth of this sequence could suggest otherwise, I'm more inclined to suspect log(a(n))/log(n) has asymptote 1. This follows a little consideration (from a statistical viewpoint) of A059339's dependency on the behavior of bigomega for extremely large numbers. - Peter Munn, Jul 29 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(1) = A059339(1) = 0; for n > 1, a(n) = A059339(n) + a(n-1).

Prog

(PARI) A374210(n) = if(n<=1, 0, A059339(n)+A374210(n-1));
(PARI)
up_to = 65537;
A059339(n) = { my(o=bigomega(n)); sum(i=1, n\2, (bigomega(i)+bigomega(n-i))==o); };
A374210list(up_to) = { my(v=vector(up_to)); v[1] = 0; for(n=2, #v, v[n] = v[n-1] + A059339(n)); (v); };
v374210 = A374210list(up_to);
A374210(n) = v374210[n];

Crossrefs

Cf. A001222, A059339.

Sequence in context: A367693 A147663 A301765 * A036811 A330265 A302163

Adjacent sequences: A374207 A374208 A374209 * A374211 A374212 A374213

Keyword

nonn

Author

Antti Karttunen and Peter Munn, Jul 28 2024

Status

approved