A376218 Odd exponentially odd numbers.

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 149

Offset

1,2

Comments

First differs from its subsequence A182318 at n = 8318: a(8318) = 19683 = 3^9 = 3^(3^2) is not a term of A182318.

Numbers whose prime factorization contains only odd primes and odd exponents.

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).

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.

The asymptotic density of this sequence is (3/5) * Product_{p prime} (1 - 1/(p*(p+1))) = (3/5) * A065463 = 0.42266532... .

Links

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

Mathematica

Select[Range[1, 150, 2], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]

Prog

(PARI) is(k) = k % 2 && vecprod(factor(k)[, 2]) % 2;

Crossrefs

Intersection of A005408 and A268335.

Cf. A057723, A065463, A182318, A307958.

Other numbers with an odd sum of divisors: A000079 (unitary divisors), A028982 (all divisors), A069562 (non-unitary divisors), A357014 (exponential divisors).

Sequence in context: A348741 A348748 A182318 * A247424 A305635 A334420

Adjacent sequences: A376215 A376216 A376217 * A376219 A376220 A376221

Keyword

nonn,easy

Author

Amiram Eldar, Sep 16 2024

Status

approved