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 A295574 a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^2. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 3 23:57 EDT 2024. Contains 374905 sequences. (Running on oeis4.)