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

1,2

Comments

From Antti Karttunen, Feb 09 2024: (Start)

Even terms in this sequence are all multiples of four.

Also natural numbers k >= 1 for which A276085(k) is a multiple of four.

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

(End)

Links

Table of n, a(n) for n=1..70.

Formula

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

Prog

(PARI) \\ See A369001

Crossrefs

Positions of even terms in A083345.

Subsequence of A368998, which is a subsequence of A235992.

Subsequence of A003159.

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

Subsequences: A046337 (odd terms in this sequence), A369005.

Sequence in context: A138299 A050435 A176656 * A369976 A345498 A248903

Adjacent sequences: A368999 A369000 A369001 * A369003 A369004 A369005

Keyword

nonn

Author

Antti Karttunen, Jan 14 2024

Status

approved