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

Author

Antti Karttunen, Jan 14 2024

Keywords

• nonn

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

Crossrefs

Positions of multiples of 27 in A083345.

Subsequence of A369003 and of A369644.

Cf. A003415, A007949.

Cf. also A377872.

Programs

PARI

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

Formula

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