# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a377001 Showing 1-1 of 1 %I A377001 #11 Oct 16 2024 21:30:54 %S A377001 4,8,32,72,94,118,128,144,147,204,284,1017,1102,1210,1462,1968,2294, %T A377001 2342,2457,2486,2670,2924,5564,6128,6368,7008,8192,10856,12216,12914, %U A377001 14066,14595,16694,18416,18825,19668,21870,22401,22713,23388,26234,26966,29038,31806 %N 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. %C A377001 Up to 10^7, the longest process takes place with 2813292 which needs 23 steps. %C A377001 Numbers of the form 2^A000043(n) or 1+A000668(n) are a subsequence. %C A377001 If we multiply instead of adding A000203(t) mod t, we get the twice even perfect numbers (A139256). %C A377001 E.g. k = 12 -> sigma(12) mod 12 = 4; sigma(4) mod 4 = 3 and 4 * 3 = 12. %e A377001 k = 72 (2 steps): %e A377001 sigma(72) mod 72 = 51; %e A377001 sigma(51) mod 51 = 21 and 51 + 21 = 72. %e A377001 k = 147 (6 steps): %e A377001 sigma(147) mod 147 = 81; %e A377001 sigma(81) mod 81 = 40; %e A377001 sigma(40) mod 40 = 10; %e A377001 sigma(10) mod 10 = 8; %e A377001 sigma(8) mod 8 = 7; %e A377001 sigma(7) mod 7 = 1 and 81 + 40 + 10 + 8 + 7 + 1 = 147. %p A377001 with(numtheory): P:=proc(q) local a,b,n,v; v:=[]; %p A377001 for n from 1 to q do a:=0; b:=n; while a