A086486 Numbers k such that the sum of the distinct prime divisors divides rad(k)=A007947(k).

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 43, 47, 49, 53, 59, 60, 61, 64, 67, 70, 71, 73, 79, 81, 83, 89, 90, 97, 101, 103, 105, 107, 109, 113, 120, 121, 125, 127, 128, 131, 137, 139, 140, 149, 150, 151, 157, 163, 167

Offset: 1

Author

Amarnath Murthy, Jul 28 2003

Keywords

• nonn
• changed

Comments

Every prime power is a member.

Numbers with exactly two distinct prime divisors are not members of the sequence. - Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003

Numbers k such that A008472(k) divides A007947(k).

Examples

			30 is a member. The prime divisors of 30 are 2, 3 and 5 and 2+3+5 = 10, divides 30.
84, however, is not a member because the sum of its distinct prime divisors (2+3+7=12) does not divide the product of its distinct prime divisors (2*3*7=42), even though 12 does divide 84. - _Harvey P. Dale_, Nov 26 2011, based on a comment from _Ray Chandler_
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A086487, A066031. A proper subset of A089352.

Programs

Mathematica

sdpQ[n_]:=Module[{dpds=Transpose[FactorInteger[n]][[1]]}, Divisible[ Times@@dpds,Total[dpds]]]; Select[Range[2,200],sdpQ] (* Harvey P. Dale, Nov 26 2011 *)

Extensions

More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003

Edited by Franz Vrabec, Sep 03 2005