A323527 Numbers whose sum of prime indices is not a perfect square.

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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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: A291880 A047426 A362781 * A316091 A026487 A130788

Adjacent sequences: A323524 A323525 A323526 * A323528 A323529 A323530

Keyword

nonn

Author

Gus Wiseman, Jan 17 2019

Status

approved