A226025 Odd composite numbers that are not squares of primes.

15, 21, 27, 33, 35, 39, 45, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, 99, 105, 111, 115, 117, 119, 123, 125, 129, 133, 135, 141, 143, 145, 147, 153, 155, 159, 161, 165, 171, 175, 177, 183, 185, 187, 189, 195, 201, 203, 205, 207, 209, 213, 215, 217

Offset

1,1

Comments

Numbers that are in A071904 (odd composite numbers) but not in A001248 (squares of primes).

First differs from its subsequence A082686 in a(16)=81 which is not in A082686. More precisely, A226025 \ A082686 = A062532 \ {1} = A014076^2 \ {1}. - M. F. Hasler, Oct 20 2013

Odd numbers that are greater than the square of their least prime factor - Odimar Fabeny, Sep 08 2014

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Formula

A226025 = { odd x>1 | A100995(x) = 0 or A100995(x) > 2 }. - M. F. Hasler, Oct 20 2013

Maple

select(n -> not(isprime(n)) and (not(issqr(n)) or not(isprime(sqrt(n)))), [seq(2*i+1, i=1..1000)]); # Robert Israel, Sep 08 2014

Mathematica

Select[Range[3, 217, 2], ! PrimeQ[#] && ! PrimeQ@Sqrt[#] &]
r = Prime@Range[2, 6]^2; Complement[Select[Range[3, Last[r] - 2, 2], ! PrimeQ[#] &], Most[r]]
Select[Range[3, 251, 2], NoneTrue[{#, Sqrt[#]}, PrimeQ]&] (* Harvey P. Dale, Sep 06 2021 *)

Prog

(Magma) [n: n in [3..217 by 2] | not IsPrime(n) and not IsSquare(n) or IsSquare(n) and not IsPrime(Floor(n^(1/2)))]
(Haskell)
a226025 n = a226025_list !! (n-1)
a226025_list = filter ((/= 2) . a100995) a071904_list
-- Reinhard Zumkeller, Jun 15 2013
(PARI) is_A226025(n)={bittest(n, 0)&&!isprime(n, 0)&&!(issquare(n)&&isprime(sqrtint(n)))&&n>1} \\ - M. F. Hasler, Oct 20 2013

Crossrefs

Subsequence of A071904. Cf. A226603.

Sequence in context: A131651 A134642 A072974 * A082686 A102030 A168104

Adjacent sequences: A226022 A226023 A226024 * A226026 A226027 A226028

Keyword

nonn

Author

Arkadiusz Wesolowski, Jun 07 2013

Status

approved