cp's OEIS Frontend

A376218 Odd exponentially odd numbers.

%I A376218 #9 Sep 16 2024 09:24:07
%S A376218 1,3,5,7,11,13,15,17,19,21,23,27,29,31,33,35,37,39,41,43,47,51,53,55,
%T A376218 57,59,61,65,67,69,71,73,77,79,83,85,87,89,91,93,95,97,101,103,105,
%U A376218 107,109,111,113,115,119,123,125,127,129,131,133,135,137,139,141,143,145,149
%N A376218 Odd exponentially odd numbers.
%C A376218 First differs from its subsequence A182318 at n = 8318: a(8318) = 19683 = 3^9 = 3^(3^2) is not a term of A182318.
%C A376218 Numbers whose prime factorization contains only odd primes and odd exponents.
%C A376218 Numbers whose sum of coreful divisors (A057723) is odd (a coreful divisor d of a number k is a divisor that is divisible by every prime that divides k, see also A307958).
%C A376218 The even exponentially odd numbers are numbers of the form 2^k * m, where k is odd and m is a term of this sequence.
%C A376218 The asymptotic density of this sequence is (3/5) * Product_{p prime} (1 - 1/(p*(p+1))) = (3/5) * A065463 = 0.42266532... .
%H A376218 Amiram Eldar, <a href="/A376218/b376218.txt">Table of n, a(n) for n = 1..10000</a>
%t A376218 Select[Range[1, 150, 2], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]
%o A376218 (PARI) is(k) = k % 2 && vecprod(factor(k)[,2]) % 2;
%Y A376218 Intersection of A005408 and A268335.
%Y A376218 Cf. A057723, A065463, A182318, A307958.
%Y A376218 Other numbers with an odd sum of divisors: A000079 (unitary divisors), A028982 (all divisors), A069562 (non-unitary divisors), A357014 (exponential divisors).
%K A376218 nonn,easy
%O A376218 1,2
%A A376218 _Amiram Eldar_, Sep 16 2024