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 A322144 a(n) = Sum_{i=1..phi(n)-1} (r(i+1)-r(i))^2 where r(1) = 1 < ... < n-1 = r(phi(n)) are the phi(n) integers relatively prime to n. 2
 0, 0, 1, 4, 3, 16, 5, 12, 11, 24, 9, 36, 11, 32, 29, 28, 15, 56, 17, 52, 39, 48, 21, 76, 31, 56, 41, 68, 27, 128, 29, 60, 59, 72, 57, 116, 35, 80, 69, 108, 39, 168, 41, 100, 95, 96, 45, 156, 59, 136, 89, 116, 51, 176, 85, 140, 99, 120, 57, 260, 59, 128, 125, 124, 99 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 Paul Erdos, Some Unconventional Problems in Number Theory, Mathematics Magazine, Vol. 52, No. 2, Mar., 1979, pp. 67-70. See Problem 12. p. 70. FORMULA a(p) = p-2, for p prime. a(k^2 * m) = k * a(k * m) + 4 * (k - 1). - David A. Corneth, Nov 28 2018 EXAMPLE a(1) and a(2) are 0, since we have an empty sum. For a(3), the integers < 3, coprime to 3, are 1 and 2, so a(3) = (2-1)^2 = 1. MATHEMATICA a[n_] := Total[Differences[Select[Range[n], GCD[n, #]==1 &]]^2]; Array[a, 50] (* Amiram Eldar, Nov 28 2018 *) PROG (PARI) a(n) = {v = select(x->gcd(x, n)==1, vector(n, k, k)); sum(i=1, #v-1, (v[i+1] - v[i])^2); } (PARI) a(n) = {my(res = 0, io = 1, in = 2); while(in < n, while(gcd(in, n) > 1, in++); res += (in - io)^2; io = in; in++); res} first(n) = {my(res = vector(n)); for(i = 1, n, c = factorback(factor(i)[, 1]); if(c == i, res[i] = a(i), res[i] = res[c] * (i / c) + 4 * (i / c - 1))); res } \\ David A. Corneth, Nov 28 2018 CROSSREFS Cf. A000010 (phi), A038566 (rows of r). Cf. A040976 (prime(n)-2), A132952 (isolated totatives). Sequence in context: A348061 A270908 A269781 * A272580 A065679 A223925 Adjacent sequences: A322141 A322142 A322143 * A322145 A322146 A322147 KEYWORD nonn AUTHOR Michel Marcus, Nov 28 2018 STATUS approved

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Last modified September 9 07:24 EDT 2024. Contains 375762 sequences. (Running on oeis4.)