A177880 Numbers k such that not all exponents in the prime power factorization of k are in A005836.

4, 9, 12, 18, 20, 25, 28, 32, 36, 44, 45, 49, 50, 52, 60, 63, 64, 68, 72, 75, 76, 84, 90, 92, 96, 98, 99, 100, 108, 116, 117, 121, 124, 126, 128, 132, 140, 144, 147, 148, 150, 153, 156, 160, 164, 169, 171, 172, 175, 180, 188, 192, 196, 198, 200, 204, 207

Offset

1,1

Comments

1 and products of distinct numbers of the form P^(3^k), k>=0, are not in the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Let A(x) be counting function of terms not exceeding x. Then for x tends to infinity, A(x)=C*x+o(x^(0.5+eps), where C=1-Prod{i=p^(3^k)with prime p and k>=0}(1-1/(i^2+i+1)).

Mathematica

Select[Range[200], AnyTrue[FactorInteger[#][[;; , 2]], DigitCount[#1, 3, 2] > 0 &] &] (* Amiram Eldar, Aug 31 2020 *)

Prog

(Sage) is_A005836 = lambda n: 2 not in n.digits(base=3)
is_A177880 = lambda n: not all(is_A005836(Integer(m)) for p, m in factor(n)) # D. S. McNeil, Dec 16 2010

Crossrefs

Cf. A005836.

Sequence in context: A089910 A344275 A312862 * A059269 A369209 A081619

Adjacent sequences: A177877 A177878 A177879 * A177881 A177882 A177883

Keyword

nonn

Author

Vladimir Shevelev, Dec 15 2010

Extensions

Extended by D. S. McNeil, Dec 16 2010

Status

approved