A382352 Numbers k such that the sum of the reciprocals of the indices of distinct prime factors of k is an integer.

1, 2, 4, 8, 16, 32, 64, 128, 195, 256, 390, 512, 585, 780, 975, 1024, 1170, 1560, 1755, 1950, 2048, 2340, 2535, 2925, 3120, 3510, 3900, 4096, 4680, 4875, 5070, 5265, 5850, 6240, 7020, 7605, 7800, 8192, 8775, 9360, 9750, 10101, 10140, 10530, 11700, 12480, 12675, 14040, 14625

Offset

1,2

Links

Table of n, a(n) for n=1..49.

Index entries for sequences computed from indices in prime factorization.

Mathematica

Join[{1}, Select[Range[2, 15000], IntegerQ[Plus @@ (1/PrimePi[#[[1]]] & /@ FactorInteger[#])] &]]

Prog

(PARI) isok(k) = my(f=factor(k)); denominator(sum(i=1, #f~, 1/primepi(f[i, 1]))) == 1; \\ Michel Marcus, Mar 22 2025

Crossrefs

Cf. A072873, A316856.

Sequence in context: A286660 A009641 A089889 * A297526 A229617 A306316

Adjacent sequences: A382349 A382350 A382351 * A382353 A382354 A382355

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2025

Status

approved