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 A344224 a(n) = Sum_{k=1..n} tau(gcd(k,n)^gcd(k,n)), where tau(n) is the number of divisors of n. 5
 1, 4, 6, 14, 10, 61, 14, 44, 33, 143, 22, 410, 26, 257, 292, 128, 34, 852, 38, 1050, 536, 581, 46, 2352, 95, 791, 162, 1978, 58, 30545, 62, 352, 1240, 1307, 1388, 6918, 74, 1613, 1700, 6264, 82, 80823, 86, 4698, 4866, 2321, 94, 12416, 189, 5790, 2836, 6490, 106, 10881, 3284, 12032, 3512, 3623 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{d|n} phi(n/d) * tau(d^d). If p is prime, a(p) = 2*p. MATHEMATICA Table[Sum[DivisorSigma[0, GCD[k, n]^(GCD[k, n])], {k, n}], {n, 100}] (* Giorgos Kalogeropoulos, May 13 2021 *) PROG (PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n)^gcd(k, n))); (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d^d)); CROSSREFS Cf. A344221, A344222, A344223, A344225. Sequence in context: A253535 A349171 A338658 * A310601 A310602 A296910 Adjacent sequences: A344221 A344222 A344223 * A344225 A344226 A344227 KEYWORD nonn AUTHOR Seiichi Manyama, May 12 2021 STATUS approved

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Last modified July 12 13:10 EDT 2024. Contains 374247 sequences. (Running on oeis4.)