A089352 Numbers that are divisible by the sum of their distinct prime factors (A008472).

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, 84, 89, 90, 97, 101, 103, 105, 107, 109, 113, 120, 121, 125, 127, 128, 131, 137, 139, 140, 149, 150, 151, 157, 163, 167, 168, 169, 173

Offset: 1

Author

Ramin Naimi (rnaimi(AT)oxy.edu), Dec 26 2003

Keywords

• easy
• nonn

Comments

The Koninck & Luca bound of x / exp(c(1 + o(1))sqrt(log x log log x)) on A158804 applies equally to this sequence. - Charles R Greathouse IV, Sep 08 2012

Examples

			84=2*2*3*7 is divisible by 2+3+7.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Jean-Marie de Koninck, Florian Luca, Integers divisible by the sum of their prime factors, Mathematika 52:1-2 (2005), pp. 69-77.

Crossrefs

Cf. A008472 (sopf).

Different from A071139.

Programs

Mathematica

primeDivisors[n_] := Select[Divisors[n], PrimeQ]; primeSumDivQ[n_] := 0 == Mod[n, Apply[Plus, primeDivisors[n]]]; Select[Range[2, 300], primeSumDivQ]
Select[Range[2, 175], Divisible[#, Plus @@ First /@ FactorInteger[#]] &] (* Jayanta Basu, Aug 13 2013 *)

PARI

is(n)=my(f=factor(n)[,1]);n%sum(i=1,#f,f[i])==0 \\ Charles R Greathouse IV, Feb 01 2013

Extensions

Name edited by Michel Marcus, Jul 15 2020