A369002 Numbers k for which k' / gcd(k,k') is even, where k' stands for the arithmetic derivative of k, A003415.

1, 9, 12, 15, 16, 20, 21, 25, 28, 33, 35, 39, 44, 49, 51, 52, 55, 57, 65, 68, 69, 76, 77, 81, 85, 87, 91, 92, 93, 95, 108, 111, 115, 116, 119, 121, 123, 124, 129, 133, 135, 141, 143, 144, 145, 148, 155, 159, 161, 164, 169, 172, 177, 180, 183, 185, 187, 188, 189, 192, 201, 203, 205, 209, 212, 213, 215, 217, 219, 221

Offset: 1

Author

Antti Karttunen, Jan 14 2024

Keywords

• nonn

Comments

From Antti Karttunen, Feb 09 2024: (Start)

Numbers k for which A276085(k) is a multiple of four.

Even terms in this sequence are all multiples of four.

A multiplicative semigroup; if m and n are in the sequence then so is m*n.

(End)

Appears to be products of an even number of terms from {4} U A065091 (counting repetitions). - Peter Munn, Jul 15 2024

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A083345, A087436, A235127, A276085, A369001 (characteristic function), A369003 (complement).

Positions of even terms in A083345.

Subsequence of A368998, which is a subsequence of A235992.

Setwise difference A003159 \ A373142.

Disjoint union of A369005 and A373265.

Disjoint union of A373138 and A373267.

Disjoint union of A369976 and A369977.

Other subsequences: A046337 (odd terms in this sequence), A373259.

Programs

PARI

\\ See A369001

Formula

For all n >= 1, A235127(a(n)) == A087436(a(n)) (mod 2). - Antti Karttunen, Feb 09 2024