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.

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..49.

Example

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.

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:=(b*add(op(2, p)/op(1, p), p=ifactors(b)[2]) 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(10^4);

Crossrefs

Cf. A003415, A377001, A377002.

Sequence in context: A147826 A247271 A065743 * A225363 A230328 A082195

Adjacent sequences: A379895 A379896 A379897 * A379899 A379900 A379901

Keyword

nonn,easy,new

Author

Paolo P. Lava, Jan 05 2025

Status

approved