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

Author

N. J. A. Sloane, Jun 08 2001

Keywords

• nonn
• easy

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

Crossrefs

A225375 is a subsequence.

Cf. A061345.

Programs

ARIBAS

for k := 3 to 253 by 2 do ar := factorlist(k); if ar[0] < ar[length(ar)-1] then write(k," ") end; end;

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 *)

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

Formula

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

Extensions

More terms from Klaus Brockhaus, Jun 10 2001