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 A275384 Composite squarefree numbers such that the arithmetic mean of its prime factors is an integer. 0
 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 EXAMPLE 170 is in the sequence because 170=17*2*5 (squarefree number) and (17+2+5)/3 = 8 is 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: A285800 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 December 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)