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A323527
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Numbers whose sum of prime indices is not a perfect square.
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4
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3, 4, 5, 6, 8, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 79, 80, 81
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The sum of prime indices of n is A056239(n).
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LINKS
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MAPLE
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remove(k-> issqr(add(numtheory[pi](i[1])*i[2], i=ifactors(k)[2])), [$1..99])[]; # Alois P. Heinz, Jan 22 2019
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MATHEMATICA
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Select[Range[100], !IntegerQ[Sqrt[Sum[PrimePi[f[[1]]]*f[[2]], {f, FactorInteger[#]}]]]&]
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PROG
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(PARI) isok(n) = {my(f=factor(n)); !issquare(sum(k=1, #f~, primepi(f[k, 1])*f[k, 2])); } \\ Michel Marcus, Jan 18 2019
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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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