A377002 -id:A377002 - cp's OEIS frontend

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

Paolo P. Lava, Oct 12 2024

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.

			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.

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

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

A379898 Integers k equal to the sum over A003415(t) mod t, for some steps, starting with t = k and then using the result to feed the next calculation.

Original entry on oeis.org

6, 24, 38, 42, 62, 96, 98, 146, 152, 162, 168, 171, 248, 384, 392, 584, 608, 648, 672, 684, 992, 1026, 1134, 1202, 1506, 1536, 1568, 1674, 2336, 2432, 2592, 2646, 2688, 2736, 3942, 3968, 4104, 4214, 4374, 4536, 4575, 4617, 4808, 6024, 6144, 6272, 6696, 9344, 9728

Offset: 1

Paolo P. Lava, Jan 05 2025

Up to 10^7, the longest process takes place with 35966, 143864, 575456, 971082, 2301824, 3884328 and 9207296 which need 8 steps.

			k = 146 (3 steps):
146' mod 146 = 75;
75' mod 75 = 55;
55' mod 55 = 16 and 75 + 55 + 16 = 146.
k = 248 (4 steps):
248' mod 248 = 132;
132' mod 132 = 56;
56' mod 56 = 36;
36' mod 36 = 24 and 132 + 56 + 36 + 24 = 248.

Cf. A003415, A377001, A377002.

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

cp's OEIS Frontend

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.

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