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

1,1

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.

Links

Table of n, a(n) for n=1..44.

Example

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.

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<n do b:=(sigma(b) mod b); if b=0 then break;
else a:=a+b; fi; od; if a=n then v:=[op(v), n]; fi; od; op(v); end: P(10^5);

Crossrefs

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

Sequence in context: A358046 A094015 A094867 * A149093 A149094 A086344

Adjacent sequences: A376998 A376999 A377000 * A377002 A377003 A377004

Keyword

nonn,easy

Author

Paolo P. Lava, Oct 12 2024

Status

approved