A227904 Numbers k such that Sum_{j=1..k} antisigma(j) == 0 (mod sigma(k)).

1, 2, 39, 78, 100, 126, 434, 501, 1313, 54111, 359466, 523219, 6601441, 8034674, 54092207, 64149290, 158882288, 3016740661, 20951813922, 52815759197, 120508871819

Offset: 1

Author

Paolo P. Lava, Oct 15 2013

Keywords

• nonn
• more

Comments

Tested up to k = 10^6.

a(22) > 2.1774*10^11. - Kevin P. Thompson, Jan 10 2022

Examples

			Sum_{j=1..39} antisigma(j) = 9408, sigma(39) = 56 and 9408 mod 56 = 0, so 39 is a term.
		

Crossrefs

Cf. A000203, A024816, A076664, A168127.

Programs

Maple

with(numtheory); P:=proc(q) local a, n; a:=0;
for n from 3 to q do a:=a+n*(n+1)/2-sigma(n);
if (a mod sigma(n))=0 then print(n); fi; od; end: P(10^9);

Extensions

a(13)-a(17) from Donovan Johnson, Oct 15 2013

a(18)-a(21) from Kevin P. Thompson, Jan 10 2022