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

1,1

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

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A008472 (sopf).

Different from A071139.

Sequence in context: A328957 A030230 A366914 * A086486 A071139 A327473

Adjacent sequences: A089349 A089350 A089351 * A089353 A089354 A089355

Keyword

easy,nonn

Author

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

Extensions

Name edited by Michel Marcus, Jul 15 2020

Status

approved