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 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), 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

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Last modified July 31 22:03 EDT 2021. Contains 346377 sequences. (Running on oeis4.)