A161769 A positive integer n is included if the greatest common divisor of (the sum of the distinct primes dividing n) and (the sum of the exponents in the prime-factorization of n) is > 1.

4, 15, 16, 21, 27, 28, 33, 35, 39, 42, 48, 51, 52, 55, 57, 60, 64, 65, 69, 72, 76, 77, 78, 84, 85, 87, 90, 91, 93, 95, 98, 105, 108, 110, 111, 114, 115, 119, 120, 123, 124, 126, 129, 132, 133, 135, 140, 141, 143, 145, 148, 150, 155, 156, 159, 161, 162, 170, 172, 175

Offset

1,1

Comments

n is included if A161606(n) is >= 2.

Links

Table of n, a(n) for n=1..60.

Example

The prime factorization of 28 is 2^2 * 7^1. The sum of the distinct prime divisors of 28 is 2+7 = 9. The sum of the prime-factorization exponents of 28 is 2+1 = 3. Since gcd(9,3) = 3 is > 1, then 28 is included in this sequence.

Mathematica

okQ[n_]:=Module[{fitr=Transpose[FactorInteger[n]]}, GCD[Plus@@First[fitr], Plus@@Last[fitr]]>1]; Select[Range[500], okQ] (* Harvey P. Dale, Jan 24 2010 *)

Crossrefs

Cf. A008472, A001222, A161606.

Sequence in context: A175959 A260577 A152442 * A135658 A228589 A066862

Adjacent sequences: A161766 A161767 A161768 * A161770 A161771 A161772

Keyword

nonn

Author

Leroy Quet, Jun 18 2009

Extensions

More terms from Harvey P. Dale, Jan 24 2010

Status

approved