A071312 Squarefree numbers k such that the largest prime factor of k is equal to the sum of the other prime factors of k.

30, 70, 286, 646, 1798, 3135, 3526, 3570, 6279, 7198, 8855, 8970, 10366, 10626, 10695, 11571, 16095, 16530, 17255, 17391, 20615, 20706, 20735, 20806, 23326, 24738, 24882, 26691, 28083, 31031, 36519, 36890, 38086, 38130, 41151, 41615

Offset: 1

Author

Benoit Cloitre, Jun 11 2002

Keywords

• easy
• nonn

Comments

If k = p(1)*p(2)*...p(r) is in the sequence, where p(r) is the largest prime factor, then p(r) = p(1)+p(2)+...+p(r-1).

Examples

			20706 = 2*3*7*17*29 and 2+3+7+17 = 29 hence 20706 is in the sequence.
		

Links

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

Crossrefs

Cf. A005117, A071141.

Programs

Mathematica

Select[Range[40000], SquareFreeQ[#] && Plus @@ (f = FactorInteger[#][[;;,1]]) == 2 * f[[-1]] &] (* Amiram Eldar, Apr 23 2022 *)

PARI

for(n=2,100000,if(issquarefree(n)*sum(i=1,omega(n)-1, component(component(factor(n),1),i))==vecmax(factor(n,1)),print1(n,",")))