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

Author

Antti Karttunen, Sep 30 2019

Keywords

• nonn

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

Crossrefs

Subsequence of A235992.

Union of A008586 and A360110.

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

Programs

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++);

Formula

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