A356413 Numbers with an equal sum of the even and odd exponents in their prime factorizations.

1, 60, 84, 90, 126, 132, 140, 150, 156, 198, 204, 220, 228, 234, 260, 276, 294, 306, 308, 315, 340, 342, 348, 350, 364, 372, 380, 414, 444, 460, 476, 490, 492, 495, 516, 522, 525, 532, 550, 558, 564, 572, 580, 585, 620, 636, 644, 650, 666, 693, 708, 726, 732, 735

Offset

1,2

Comments

Numbers k such that A350386(k) = A350387(k).

A085987 is a subsequence. Terms that are not in A085987 are 1, 2160, 3024, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

60 is a term since A350386(60) = A350387(60) = 2.

Mathematica

f[p_, e_] := (-1)^e*e; q[1] = True; q[n_] := Plus @@ f @@@ FactorInteger[n] == 0; Select[Range[1000], q]

Prog

(PARI) isok(n) = {my(f = factor(n)); sum(i = 1, #f~, (-1)^f[i, 2]*f[i, 2]) == 0};

Crossrefs

Cf. A350386, A350387.

Subsequence of A028260.

Subsequences: A085987, A179698, A190109, A190110.

Similar sequences: A048109, A187039, A348097.

Sequence in context: A009129 A174292 A085987 * A086974 A099831 A306222

Adjacent sequences: A356410 A356411 A356412 * A356414 A356415 A356416

Keyword

nonn

Author

Amiram Eldar, Aug 06 2022

Status

approved