A378481 - OEIS

%I #6 Jun 02 2025 15:28:45

%S 33,77,153,372,1540,2300,2692,2736,7812,8721,12593,26025,26481,27972,

%T 39321,64009,104409,175441,325180,335616,422593,455625,564376,575040,

%U 756460,800073,1104521,2180545,2304332,3502665,3691968,5130909,5515121,9331441,9546265

%N Integers k such that A378414(k) == k (mod A066417(k)).

%C Also integers k such that A000217(k) == k (mod A066417(k)).

%C So far, only 33 belongs both to A232538 and A378414.

%e Antidivisors of 77 are 2, 3, 5, 9, 14, 17, 22, 31, 51 and their sum is 154.

%e Then 77*78/2 mod 154 = 3003 mod 154 = 77.

%p with(numtheory): P:=proc(q) local j,k,n,v; v:=[];

%p 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 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 then v:=[op(v),n]; fi; od; op(v); end: P(10^5);

%Y Cf. A000217, A066417, A232538, A378414.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Nov 28 2024