A377001 Integers k equal to the sum over A000203(t) mod t, for some steps, starting with t = k and then using the result to feed the next calculation.

4, 8, 32, 72, 94, 118, 128, 144, 147, 204, 284, 1017, 1102, 1210, 1462, 1968, 2294, 2342, 2457, 2486, 2670, 2924, 5564, 6128, 6368, 7008, 8192, 10856, 12216, 12914, 14066, 14595, 16694, 18416, 18825, 19668, 21870, 22401, 22713, 23388, 26234, 26966, 29038, 31806

Offset: 1

Author

Paolo P. Lava, Oct 12 2024

Keywords

• nonn
• easy

Comments

Up to 10^7, the longest process takes place with 2813292 which needs 23 steps.

Numbers of the form 2^A000043(n) or 1+A000668(n) are a subsequence.

If we multiply instead of adding A000203(t) mod t, we get the twice even perfect numbers (A139256).

E.g. k = 12 -> sigma(12) mod 12 = 4; sigma(4) mod 4 = 3 and 4 * 3 = 12.

Examples

			k = 72 (2 steps):
sigma(72) mod 72 = 51;
sigma(51) mod 51 = 21 and 51 + 21 = 72.
k = 147  (6 steps):
sigma(147) mod 147 = 81;
sigma(81) mod 81 = 40;
sigma(40) mod 40 = 10;
sigma(10) mod 10 = 8;
sigma(8) mod 8 = 7;
sigma(7) mod 7 = 1 and 81 + 40 + 10 + 8 + 7 + 1 = 147.
		

Crossrefs

Cf. A000043, A000203, A000668, A139256, A377002.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,n,v; v:=[];
for n from 1 to q do a:=0; b:=n; while a