A119251 Positive integers each with exactly 1 unitary prime divisor (i.e., n is included if and only if A056169(n) = 1).

2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 20, 23, 24, 28, 29, 31, 37, 40, 41, 43, 44, 45, 47, 48, 50, 52, 53, 54, 56, 59, 61, 63, 67, 68, 71, 73, 75, 76, 79, 80, 83, 88, 89, 92, 96, 97, 98, 99, 101, 103, 104, 107, 109, 112, 113, 116, 117, 124, 127, 131, 135, 136, 137, 139, 147

Offset

1,1

Comments

Also, numbers expressible as the product of a prime and a powerful number not divisible by that prime. - Franklin T. Adams-Watters, Jul 25 2006

a(n) << n log n since all primes are in this sequence and it should not be hard to show that a(n) >> n log n. I believe a(n) ~ k*n*log n but cannot prove this. - Charles R Greathouse IV, Dec 22 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

28 has the prime factorization of 2^2 * 7^1. 28 is therefore included in this sequence because there is exactly one prime raised to an exponent of 1 in 28's prime factorization.

Mathematica

Select[Range@147, Count[FactorInteger@#, 1, 2] == 1 &] (* Robert G. Wilson v, Jul 25 2006 *)

Prog

(PARI) list(lim)=my(v=List()); lim\=1; forsquarefree(m=1, sqrtnint(lim\2, 3), my(c=m[1]^3); for(n=1, sqrtint(lim\(2*c)), my(t=c*n^2); forprime(p=2, lim\t, if(t%p, listput(v, t*p))))); Set(v) \\ Charles R Greathouse IV, Dec 22 2025

Crossrefs

Cf. A001694, A056169.

Sequence in context: A073085 A340657 A316793 * A385998 A182358 A336418

Adjacent sequences: A119248 A119249 A119250 * A119252 A119253 A119254

Keyword

nonn

Author

Leroy Quet, Jul 23 2006

Extensions

More terms from Robert G. Wilson v and Franklin T. Adams-Watters, Jul 25 2006

Status

approved