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

1,1

Links

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

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

Example

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.

Mathematica

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

Prog

(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(k=1, logint(lim\9, 2), my(L=lim>>k); for(e=2, logint(L, 3), forprime(p=3, sqrtnint(L, e), listput(v, p^e<<k)))); for(k=1, logint(lim\3, 2), forprime(p=3, lim>>k, listput(v, p<<k))); Set(v) \\ Charles R Greathouse IV, Dec 13 2021

Crossrefs

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

Sequence in context: A141098 A084563 A194396 * A284788 A323288 A322131

Adjacent sequences: A321190 A321191 A321192 * A321194 A321195 A321196

Keyword

nonn,easy

Author

Lei Zhou, Oct 29 2018

Status

approved