A369002 - OEIS

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

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OFFSET

1,2

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

FORMULA

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

PROG

(PARI) \\ See A369001

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.

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