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A226025 Odd composite numbers that are not squares of primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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]]

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

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Last modified January 29 14:23 EST 2020. Contains 331338 sequences. (Running on oeis4.)