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A275384
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Composite squarefree numbers such that the arithmetic mean of its prime factors is an integer.
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1
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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
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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170 is in the sequence because 170 = 17*2*5 (squarefree number) and (17+2+5)/3 = 8 is an integer.
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MATHEMATICA
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Select[Range@ 270, And[CompositeQ@ #, SquareFreeQ@ #, IntegerQ@ Mean@ FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Jul 25 2016 *)
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PROG
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(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, ", "))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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