A061346 Odd numbers that are neither primes nor prime powers.

15, 21, 33, 35, 39, 45, 51, 55, 57, 63, 65, 69, 75, 77, 85, 87, 91, 93, 95, 99, 105, 111, 115, 117, 119, 123, 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, 219, 221

Offset

1,1

Comments

Odd numbers with at least two distinct prime factors. - N. J. A. Sloane, Oct 15 2022

Odd leg of more than one primitive Pythagorean triangles. For smallest odd leg common to 2^n PPTs, see A070826. - Lekraj Beedassy, Jul 12 2006

Numbers that can be factored by Shor's algorithm. - Charles R Greathouse IV, Mar 05 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ 2n. - Charles R Greathouse IV, Aug 20 2012

Maple

select(t -> nops(ifactors(t)[2]) > 1, [seq(2*i+1, i=1..1000)]); # Robert Israel, Dec 14 2014

Mathematica

Select[Range[1, 249, 2], Length[FactorInteger[#]] > 1 &] (* Alonso del Arte, Jan 30 2012 *)
Select[ Range[1, 475, 2], PrimeNu@# > 1 &] (* Robert G. Wilson v, Dec 12 2014 *)

Prog

(ARIBAS): for k := 3 to 253 by 2 do ar := factorlist(k); if ar[0] < ar[length(ar)-1] then write(k, " ") end; end;
(PARI) is(n)=ispower(n, , &n); n%2&&!isprime(n)&&n>1 \\ Charles R Greathouse IV, Jan 30 2012
(PARI) is(n)=n%2 && !isprimepower(n) && n>1 \\ Charles R Greathouse IV, May 06 2016
(PARI) count(x)=if(x<9, 0, (x\=1) - sum(k=1, logint(x, 3), primepi(sqrtnint(x, k)) - 1) - x\2 - 1) \\ Charles R Greathouse IV, Mar 06 2018

Crossrefs

A225375 is a subsequence.

Cf. A061345.

Sequence in context: A070005 A275384 A185307 * A098905 A225375 A329229

Adjacent sequences: A061343 A061344 A061345 * A061347 A061348 A061349

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 08 2001

Extensions

More terms from Klaus Brockhaus, Jun 10 2001

Status

approved