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A323527 Numbers whose sum of prime indices is not a perfect square. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..66.

MAPLE

remove(k-> issqr(add(numtheory[pi](i[1])*i[2], i=ifactors(k)[2])), [$1..99])[];  # Alois P. Heinz, Jan 22 2019

MATHEMATICA

Select[Range[100], !IntegerQ[Sqrt[Sum[PrimePi[f[[1]]]*f[[2]], {f, FactorInteger[#]}]]]&]

PROG

(PARI) isok(n) = {my(f=factor(n)); !issquare(sum(k=1, #f~, primepi(f[k, 1])*f[k, 2])); } \\ Michel Marcus, Jan 18 2019

CROSSREFS

Complement of A323528.

Cf. A000037, A000720, A001248, A026478 (Omega is square), A056239, A112798, A323520, A323521 (Omega is not square), A323525, A323526.

Sequence in context: A023367 A291880 A047426 * A316091 A026487 A130788

Adjacent sequences:  A323524 A323525 A323526 * A323528 A323529 A323530

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 17 2019

STATUS

approved

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Last modified September 21 20:10 EDT 2021. Contains 347598 sequences. (Running on oeis4.)