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A377872
Numbers k for which A276085(k) is a multiple of 27, where A276085 is fully additive with a(p) = p#/p.
9
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
1,2
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)
FORMULA
{k such that Sum e*A377876(A000720(p)-1) == 0 (mod 27), when k = Product(p^e)}.
PROG
(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)); };
CROSSREFS
Subsequence of A339746, and of A377873.
Cf. also A369007, A377875.
Sequence in context: A063131 A128880 A039596 * A013543 A115377 A146145
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 10 2024
STATUS
approved