cp's OEIS Frontend

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

%I A369002 #38 Jul 15 2024 15:33:00
%S A369002 1,9,12,15,16,20,21,25,28,33,35,39,44,49,51,52,55,57,65,68,69,76,77,
%T A369002 81,85,87,91,92,93,95,108,111,115,116,119,121,123,124,129,133,135,141,
%U A369002 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
%N A369002 Numbers k for which k' / gcd(k,k') is even, where k' stands for the arithmetic derivative of k, A003415.
%C A369002 From _Antti Karttunen_, Feb 09 2024: (Start)
%C A369002 Numbers k for which A276085(k) is a multiple of four.
%C A369002 Even terms in this sequence are all multiples of four.
%C A369002 A multiplicative semigroup; if m and n are in the sequence then so is m*n.
%C A369002 (End)
%C A369002 Appears to be products of an even number of terms from {4} U A065091 (counting repetitions). - _Peter Munn_, Jul 15 2024
%H A369002 Antti Karttunen, <a href="/A369002/b369002.txt">Table of n, a(n) for n = 1..10000</a>
%F A369002 For all n >= 1, A235127(a(n)) == A087436(a(n)) (mod 2). - _Antti Karttunen_, Feb 09 2024
%o A369002 (PARI) \\ See A369001
%Y A369002 Cf. A003415, A083345, A087436, A235127, A276085, A369001 (characteristic function), A369003 (complement).
%Y A369002 Positions of even terms in A083345.
%Y A369002 Subsequence of A368998, which is a subsequence of A235992.
%Y A369002 Setwise difference A003159 \ A373142.
%Y A369002 Disjoint union of A369005 and A373265.
%Y A369002 Disjoint union of A373138 and A373267.
%Y A369002 Disjoint union of A369976 and A369977.
%Y A369002 Other subsequences: A046337 (odd terms in this sequence), A373259.
%K A369002 nonn
%O A369002 1,2
%A A369002 _Antti Karttunen_, Jan 14 2024