This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378481 #6 Jun 02 2025 15:28:45 %S A378481 33,77,153,372,1540,2300,2692,2736,7812,8721,12593,26025,26481,27972, %T A378481 39321,64009,104409,175441,325180,335616,422593,455625,564376,575040, %U A378481 756460,800073,1104521,2180545,2304332,3502665,3691968,5130909,5515121,9331441,9546265 %N A378481 Integers k such that A378414(k) == k (mod A066417(k)). %C A378481 Also integers k such that A000217(k) == k (mod A066417(k)). %C A378481 So far, only 33 belongs both to A232538 and A378414. %e A378481 Antidivisors of 77 are 2, 3, 5, 9, 14, 17, 22, 31, 51 and their sum is 154. %e A378481 Then 77*78/2 mod 154 = 3003 mod 154 = 77. %p A378481 with(numtheory): P:=proc(q) local j,k,n,v; v:=[]; %p A378481 for n from 3 to q do k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od; %p A378481 if n*(n+1)/2 mod (sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2)=n %p A378481 then v:=[op(v),n]; fi; od; op(v); end: P(10^5); %Y A378481 Cf. A000217, A066417, A232538, A378414. %K A378481 nonn,easy %O A378481 1,1 %A A378481 _Paolo P. Lava_, Nov 28 2024