A377001 -id:A377001 - cp's OEIS frontend

A377002 Integers k equal to the sum over A024816(t) mod t, for some steps, starting with t = k and then using the result to feed the next calculation.

9, 20, 60, 78, 81, 117, 120, 136, 244, 261, 385, 532, 608, 1568, 2247, 2704, 2949, 4352, 5952, 6084, 6564, 10972, 15688, 17524, 20356, 21066, 21868, 42771, 58045, 92034, 103660, 108333, 145203, 196869, 201963, 225021, 226626, 232300, 263133, 309603, 431640, 497380

Offset: 1

Paolo P. Lava, Oct 12 2024

Up to 10^7, the longest process takes place with 823002 which needs 26 steps.

			k = 78  (7 steps):
(78*79/2-sigma(78)) mod 78 = 27;
(27*28/2-sigma(27)) mod 27 = 14;
(14*15/2-sigma(14)) mod 14 = 11;
(11*12/2-sigma(11)) mod 11 = 10;
(10*11/2-sigma(10)) mod 10 = 7;
(7*8/2-sigma(7)) mod 7 = 6;
(6*7/2-sigma(6)) mod 6 = 3 and 27 + 14 + 11 + 10 + 7 + 6 + 3 = 78.

Cf. A000203, A024816, A377001.

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

A377002 Integers k equal to the sum over A024816(t) mod t, for some steps, starting with t = k and then using the result to feed the next calculation.

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