cp's OEIS Frontend

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

%I A377872 #44 Nov 17 2024 13:07:10
%S A377872 1,55,95,115,155,174,187,203,232,265,282,297,323,325,329,335,376,391,
%T A377872 396,438,462,474,511,513,515,527,528,539,553,584,606,616,621,632,649,
%U A377872 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
%N A377872 Numbers k for which A276085(k) is a multiple of 27, where A276085 is fully additive with a(p) = p#/p.
%C A377872 A multiplicative semigroup; if m and n are in the sequence then so is m*n.
%C A377872 From _Antti Karttunen_, Nov 17 2024: (Start)
%C A377872 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.
%C A377872 If 3*x is a term, then 4*x is also a term, and vice versa.
%C A377872 Contains no even semiprimes (A100484), semiprimes of the form 3*prime (A001748), nor terms of the form 4*prime (A001749).
%C A377872 (End)
%H A377872 Antti Karttunen, <a href="/A377872/b377872.txt">Table of n, a(n) for n = 1..12000</a>
%H A377872 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A377872 {k such that Sum e*A377876(A000720(p)-1) == 0 (mod 27), when k = Product(p^e)}.
%o A377872 (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)); };
%Y A377872 Cf. A276085, A377869, A377876, A377878.
%Y A377872 Subsequence of A339746, and of A377873.
%Y A377872 Cf. also A369007, A377875.
%K A377872 nonn
%O A377872 1,2
%A A377872 _Antti Karttunen_, Nov 10 2024