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 A277793 Numbers k such that the arithmetic and geometric means of the divisors of k are both integers. 3
 1, 49, 169, 361, 961, 1369, 1849, 3721, 4489, 5329, 6241, 8281, 9409, 10609, 11881, 14641, 16129, 17689, 19321, 22801, 24649, 26569, 32761, 37249, 39601, 44521, 47089, 49729, 52441, 58081, 61009, 67081, 73441, 76729, 80089, 87616, 90601, 94249, 97969, 109561, 113569, 121801, 134689 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Intersection of A000290 and A003601. Union of squares of A107924 and squares of A107925. The squares of the primes == 1 (mod 6), squares of A002476, are a subsequence: 49, 169, 361,... - R. J. Mathar, May 19 2020 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Divisor Wikipedia, Arithmetic number Index entries for sequences related to sums of divisors EXAMPLE a(2) = 49 because 49 has 3 divisors {1,7,49} therefore (1 + 7 + 49)/3 = 19 and (1*7*49)^(1/3) = 7 are both integers. MATHEMATICA Select[Range[140000], Divisible[DivisorSigma[1, #1], DivisorSigma[0, #1]] && Mod[DivisorSigma[0, #1], 2] == 1 & ] Select[Range[150000], AllTrue[{Mean[Divisors[#]], GeometricMean[ Divisors[ #]]}, IntegerQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 21 2018 *) CROSSREFS Cf. A000290, A003601, A107924, A107925. Sequence in context: A254624 A256074 A016922 * A147608 A258060 A039686 Adjacent sequences: A277790 A277791 A277792 * A277794 A277795 A277796 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Oct 31 2016 STATUS approved

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Last modified November 30 03:37 EST 2023. Contains 367452 sequences. (Running on oeis4.)