A327864 Numbers whose arithmetic derivative is a multiple of 4, cf. A003415.

0, 1, 4, 8, 12, 15, 16, 20, 24, 28, 32, 35, 36, 39, 40, 44, 48, 51, 52, 55, 56, 60, 64, 68, 72, 76, 80, 81, 84, 87, 88, 91, 92, 95, 96, 100, 104, 108, 111, 112, 115, 116, 119, 120, 123, 124, 128, 132, 136, 140, 143, 144, 148, 152, 155, 156, 159, 160, 164, 168, 172, 176, 180, 183, 184, 187, 188, 189, 192, 196, 200, 203

Offset

1,3

Comments

Also k such that A359423(k) is a multiple of 4. - Antti Karttunen, Jan 02 2023

A multiplicative semigroup; if m and n are in the sequence then so is m*n. - Antti Karttunen, Feb 01 2023

Links

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

Formula

{k | A353493(k)=0}. - Antti Karttunen, Jan 02 2023

Prog

(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
isA327864(n) = !(A003415(n)%4);
k=1; n=0; while(k<105, if(isA327864(n), print1(n, ", "); k++); n++);

Crossrefs

Subsequence of A235992.

Union of A008586 and A360110.

Cf. A003415, A327862, A327863, A327865, A353493, A353494 (characteristic function), A359423.

Sequence in context: A009023 A099309 A327929 * A235865 A311086 A311087

Adjacent sequences: A327861 A327862 A327863 * A327865 A327866 A327867

Keyword

nonn

Author

Antti Karttunen, Sep 30 2019

Status

approved