A377872 Numbers k for which A276085(k) is a multiple of 27, where A276085 is fully additive with a(p) = p#/p.

1, 55, 95, 115, 155, 174, 187, 203, 232, 265, 282, 297, 323, 325, 329, 335, 376, 391, 396, 438, 462, 474, 511, 513, 515, 527, 528, 539, 553, 584, 606, 616, 621, 632, 649, 654, 678, 684, 704, 707, 745, 763, 791, 798, 808, 828, 837, 872, 901, 904, 906, 912, 913, 931, 966, 978, 1002, 1057, 1064, 1073, 1074, 1075, 1104, 1105

Offset: 1

Author

Antti Karttunen, Nov 10 2024

Keywords

• nonn

Comments

A multiplicative semigroup; if m and n are in the sequence then so is m*n.

From Antti Karttunen, Nov 17 2024: (Start)

Question: What is the asymptotic density of this sequence? There are 1, 3, 56, 484, 4899, 50034, 508254 terms <= 10^k, for k=1..7. See also questions in A377869 and in A377878.

If 3*x is a term, then 4*x is also a term, and vice versa.

Contains no even semiprimes (A100484), semiprimes of the form 3*prime (A001748), nor terms of the form 4*prime (A001749).

(End)

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A276085, A377869, A377876, A377878.

Subsequence of A339746, and of A377873.

Cf. also A369007, A377875.

Programs

PARI

isA377872(n) = { my(m=27, f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= Mod(prime(i),m); i++); s += f[k, 2]*pr); (0==lift(s)); };

Formula

{k such that Sum e*A377876(A000720(p)-1) == 0 (mod 27), when k = Product(p^e)}.