A338930 -id:A338930 - cp's OEIS frontend

A338935 a(n) = Sum_{d|n} (d^2 mod n).

0, 1, 1, 1, 1, 8, 1, 5, 1, 10, 1, 18, 1, 12, 20, 5, 1, 23, 1, 26, 17, 16, 1, 58, 1, 18, 10, 42, 1, 70, 1, 21, 32, 22, 40, 39, 1, 24, 23, 90, 1, 106, 1, 54, 71, 28, 1, 98, 1, 55, 44, 34, 1, 104, 37, 106, 29, 34, 1, 240, 1, 36, 77, 21, 65, 160, 1, 38, 56, 200, 1, 175, 1, 42, 60, 78, 94, 154, 1, 146

Offset: 1

J. M. Bergot and Robert Israel, Nov 16 2020

nonn

			a(6) = (1^2 mod 6) + (2^2 mod 6) + (3^2 mod 6) + (6^2 mod 6) = 1+4+3+0 = 8.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000430 (a(n)=1), A338930 (a(n) is prime).

f:= n -> add(t^2 mod n, t = numtheory:-divisors(n)):
map(f, [$1..100]);

Table[Total[Mod[Divisors[n]^2,n]],{n,80}] (* Harvey P. Dale, Oct 11 2021 *)

a(n) = sumdiv(n, d, lift(Mod(d, n)^2)); \\ Michel Marcus, Nov 16 2020

A338936 Primes in A338935.

Original entry on oeis.org

5, 5, 23, 17, 23, 71, 37, 29, 41, 103, 113, 71, 47, 101, 53, 359, 227, 293, 71, 79, 67, 83, 709, 89, 271, 149, 643, 107, 113, 401, 97, 257, 137, 227, 149, 1051, 167, 577, 263, 173, 127, 269, 839, 263, 191, 599, 359, 1399, 401, 709, 659, 1213, 157, 233, 359, 239, 223, 577, 353, 727, 251, 677, 257

Offset: 1

J. M. Bergot and Robert Israel, Nov 16 2020

nonn

			a(3) = A338935(18) = 23 is the third prime in A338935.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A338930, A338935.

f:= n -> add(t^2 mod n, t = numtheory:-divisors(n)):
select(isprime, map(f, [$1..1000]));

a(n) = A338935(A338930(n)).

cp's OEIS Frontend

A338935 a(n) = Sum_{d|n} (d^2 mod n).

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