A275384 - OEIS

A275384

Composite squarefree numbers such that the arithmetic mean of its prime factors is an integer.

15, 21, 33, 35, 39, 42, 51, 55, 57, 65, 69, 77, 78, 85, 87, 91, 93, 95, 105, 110, 111, 114, 115, 119, 123, 129, 133, 141, 143, 145, 155, 159, 161, 170, 177, 183, 185, 186, 187, 195, 201, 203, 205, 209, 213, 215, 217, 219, 221, 222, 230, 231, 235, 237, 247, 249, 253, 258, 259, 265, 267

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OFFSET

1,1

COMMENTS

Sopf(a(n)) is multiple of omega(a(n)) (sopf(n) is the sum of the distinct prime factors of n, and omega(n) is the number of distinct primes dividing n).

This sequence is subsequence of A078177 and supersequence of A187073.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

170 is in the sequence because 170 = 17*2*5 (squarefree number) and (17+2+5)/3 = 8 is an integer.

MATHEMATICA

Select[Range@ 270, And[CompositeQ@ #, SquareFreeQ@ #, IntegerQ@ Mean@ FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Jul 25 2016 *)

PROG

(PARI) sopf(n)= my(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); s

for(i=2, 500, if(issquarefree(i)&&!isprime(i), m=sopf(i)/omega(i); if(m==truncate(m), print1(i, ", "))))

CROSSREFS

Cf. A005117, A078177, A134344, A187073, A229094.