

A078177


Composite numbers with an integer arithmetic mean of all prime factors.


4



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
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OFFSET

1,1


COMMENTS

That is, composite numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is an integer.


LINKS

Table of n, a(n) for n=1..61.


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.


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, A134330, A134331, A134332, A134333, A134334, A134344, A134376.
Sequence in context: A122785 A280450 A137055 * A023886 A158337 A161542
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



