A295574 a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^2.

0, 1, 1, 1, 5, 1, 14, 10, 21, 10, 55, 26, 91, 35, 70, 84, 204, 75, 285, 140, 210, 165, 506, 196, 525, 286, 549, 406, 1015, 340, 1240, 680, 880, 680, 1190, 654, 2109, 969, 1482, 1080, 2870, 966, 3311, 1650, 2010, 1771, 4324, 1544, 4214, 2050

Offset

1,5

Comments

n does not divide a(n) iff n = (2^k)*(q^m) with k > 0, m >= 0 and q odd prime such that q == 3 (mod 4) or n = (2^k)*(3^L)*Product_{q} q^(v_q) with k >= 0, L > 0, v_q >= 0 and all q odd primes such that q == 5 (mod 6). - René Gy, Oct 21 2018

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

John D. Baum, A Number-Theoretic Sum, Mathematics Magazine 55.2 (1982): 111-113.

René Gy, The sum of product pairs of integers prime to n, Math StackExchange.

Maple

R:=proc(n, k) local x, t1, S;
t1:={}; S:=0;
for x from 1 to floor(n/2) do if gcd(x, n)=1 then t1:={op(t1), x^k}; S:=S+x^k; fi; od;
S; end;
s:=k->[seq(R(n, k), n=1..50)];
s(2);

Mathematica

f[n_] := Plus @@ (Select[ Range[n/2], GCD[#, n] == 1 &]^2); Array[f, 50] (* Robert G. Wilson v, Dec 10 2017 *)

Prog

(PARI) a(n) = sum(j=1, n\2, (gcd(j, n)==1)*j^2); \\ Michel Marcus, Dec 10 2017

Crossrefs

In the Baum (1982) paper, S_1, S_2, S_3, S_4 are A023896, A053818, A053819, A053820, and S'_1, S'_2, S'_3, S'_4 are A066840, A295574, A295575, A295576.

Cf. A023022.

Sequence in context: A120393 A370518 A094368 * A087727 A039807 A213590

Adjacent sequences: A295571 A295572 A295573 * A295575 A295576 A295577

Keyword

nonn

Author

N. J. A. Sloane, Dec 08 2017

Status

approved