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 A078177 Composite numbers with an integer arithmetic mean of all prime factors. 5
 4, 8, 9, 15, 16, 20, 21, 25, 27, 32, 33, 35, 39, 42, 44, 49, 50, 51, 55, 57, 60, 64, 65, 68, 69, 77, 78, 81, 85, 87, 91, 92, 93, 95, 105, 110, 111, 112, 114, 115, 116, 119, 121, 123, 125, 128, 129, 133, 140, 141, 143, 145, 155, 156, 159, 161, 164, 169, 170, 177, 180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS That is, composite numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is an integer. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA A001414(a(n)) == 0 modulo A001222(a(n)). EXAMPLE 60 = 2*2*3*5: (2+2+3+5)/4 = 3, therefore 60 is a term. MATHEMATICA Select[Range[200], CompositeQ[#] && IntegerQ[Mean[Flatten[Table[#[[1]], #[[2]]]& /@ FactorInteger[#]]]]&] (* Jean-François Alcover, Aug 03 2018 *) PROG (PARI) lista(nn) = {forcomposite(n=1, nn, my(f = factor(n)); if (! (sum(k=1, #f~, f[k, 1]*f[k, 2]) % vecsum(f[, 2])), print1(n, ", ")); ); } \\ Michel Marcus, Feb 22 2016 CROSSREFS Cf. A078175, A001222, A100118, A046363, A133620, A133621. Cf. A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134334, A134344, A134376. Sequence in context: A122785 A280450 A137055 * A326692 A373375 A336663 Adjacent sequences: A078174 A078175 A078176 * A078178 A078179 A078180 KEYWORD nonn AUTHOR Reinhard Zumkeller, Nov 20 2002 EXTENSIONS Edited by N. J. A. Sloane, May 30 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified August 6 07:07 EDT 2024. Contains 374960 sequences. (Running on oeis4.)