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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.
1
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.
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
KEYWORD
easy,nonn
AUTHOR
Paolo P. Lava, Oct 12 2024
STATUS
approved