A321193 Even numbers with no more than one odd prime factor, not counting multiplicity.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 56, 58, 62, 64, 68, 72, 74, 76, 80, 82, 86, 88, 92, 94, 96, 98, 100, 104, 106, 108, 112, 116, 118, 122, 124, 128, 134, 136, 142, 144, 146, 148, 152, 158, 160, 162, 164, 166, 172, 176, 178, 184, 188, 192, 194, 196

Offset: 1

Author

Lei Zhou, Oct 29 2018

Keywords

• nonn
• easy

Examples

			18 = 2 * 3^2 is in the sequence because it has 1 odd prime factor (3 counts only once).
16 = 2^4 is in the sequence because it has no odd prime factors.
70 = 2 * 5 * 7 is not in the sequence because it has 2 odd prime factors.
		

Links

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

Crossrefs

Cf. A070776, A100367, A001221, A098902, A100368.

Programs

Mathematica

n = 0; Table[n = n + 2;
While[Length[FactorInteger[n]] > 2, n = n + 2]; n, {k, 1, 76}]

PARI

is(n) = n%2==0 && omega(n) <= 2 \\ Felix Fröhlich, Nov 01 2018

PARI

is(n)=my(o=valuation(n,2)); o && isprimepower(n>>o) \\ Charles R Greathouse IV, Dec 13 2021

PARI

list(lim)=my(v=List()); for(k=1,logint(lim\=1,2), listput(v,1<>k); for(e=2,logint(L,3), forprime(p=3, sqrtnint(L,e), listput(v,p^e<>k, listput(v,p<Charles R Greathouse IV, Dec 13 2021

Formula

Numbers of the form 2^k*p^h where k > 0, h >= 0 p is an odd prime.

a(n) = 2 * A070776(n-1) for n > 1. - Alois P. Heinz, Nov 20 2018