

A275384


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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.
Sequence in context: A340380 A184041 A070005 * A185307 A061346 A098905
Adjacent sequences: A275381 A275382 A275383 * A275385 A275386 A275387


KEYWORD

nonn


AUTHOR

Antonio Roldán, Jul 25 2016


STATUS

approved



