A158804 Composite integers that are a multiple of the sum of their distinct prime factors.

4, 8, 9, 16, 25, 27, 30, 32, 49, 60, 64, 70, 81, 84, 90, 105, 120, 121, 125, 128, 140, 150, 168, 169, 180, 231, 234, 240, 243, 252, 256, 260, 270, 280, 286, 289, 300, 315, 336, 343, 350, 360, 361, 450, 456, 468, 480, 490, 504, 512, 520, 525, 528, 529, 532, 540

Offset

1,1

Comments

Koninck & Luca give upper and lower bounds for the number of elements of this sequence below x: x / exp(c_i(1 + o(1))sqrt(log x log log x)), where the constants c_i and the o(1) differ for lower and upper bounds. - 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) 69-77, MR2261843.

Formula

{n in A002808: A008472(n)|n }

Example

4 is in the sequence because A008472(4)=2 divides 4. 5 is not in the sequence because it is prime. 6 is not in the sequence because A008472(6)=5 does not divide 6.

Maple

A008472 := proc(n) numtheory[factorset](n) ; add(d, d=%) ; end: isbeta := proc(n) if isprime(n) then false; else if n mod A008472(n) = 0 then true; else false; fi; fi; end: for n from 2 to 1200 do if isbeta(n) then printf("%d, ", n); fi; od:

Mathematica

Select[Range[2, 540], !PrimeQ[#]&&IntegerQ[#/Total[First/@FactorInteger[#]]]&] (* Jayanta Basu, Jun 02 2013 *)

Prog

(PARI) is(n)=my(f=factor(n)[, 1]); n%sum(i=1, #f, f[i])==0 \\ Charles R Greathouse IV, Feb 04 2013

Crossrefs

Cf. A002808 (composite numbers), A008472.

Sequence in context: A140104 A127398 A109422 * A341645 A339497 A348121

Adjacent sequences: A158801 A158802 A158803 * A158805 A158806 A158807

Keyword

easy,nonn

Author

R. J. Mathar, Mar 27 2009

Status

approved