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

1,1

Comments

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

Links

Table of n, a(n) for n=1..42.

Example

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.

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*(b+1)/2-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(5*10^5);

Crossrefs

Cf. A000203, A024816, A377001.

Sequence in context: A109805 A345727 A332372 * A344818 A341529 A013573

Adjacent sequences: A376999 A377000 A377001 * A377003 A377004 A377005

Keyword

easy,nonn

Author

Paolo P. Lava, Oct 12 2024

Status

approved