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

Author

Vladimir Shevelev, Dec 15 2010

Keywords

• nonn

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

Crossrefs

Cf. A005836.

Programs

Mathematica

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

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

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)).

Extensions

Extended by D. S. McNeil, Dec 16 2010