A369007 Numbers k for which k' / gcd(k,k') is a multiple of 27, where k' stands for the arithmetic derivative of k, A003415(k).

1, 158, 160, 208, 212, 275, 329, 374, 410, 428, 473, 482, 515, 533, 629, 698, 700, 707, 713, 785, 910, 914, 952, 1055, 1058, 1067, 1072, 1076, 1078, 1080, 1183, 1204, 1238, 1346, 1404, 1431, 1445, 1454, 1490, 1562, 1661, 1691, 1724, 1813, 1841, 1865, 1888, 1937, 1994, 2102, 2219, 2291, 2320, 2372, 2426, 2432, 2570

Offset

1,2

Comments

Question: What is the asymptotic density of these terms? 0.0253...?

A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - Antti Karttunen, Nov 11 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

For all n >= 1, A007949(a(n)) = 3*k, for k >= 0. - Antti Karttunen, Nov 12 2024

Prog

(PARI)
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
isA369007(n) = !(A083345(n)%27);

Crossrefs

Positions of multiples of 27 in A083345.

Subsequence of A369003 and of A369644.

Cf. A003415, A007949.

Cf. also A377872.

Sequence in context: A074220 A015265 A260447 * A345511 A048930 A130864

Adjacent sequences: A369004 A369005 A369006 * A369008 A369009 A369010

Keyword

nonn

Author

Antti Karttunen, Jan 14 2024

Status

approved