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A158804 Composite integers that are a multiple of the sum of their distinct prime factors. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A080366

Adjacent sequences:  A158801 A158802 A158803 * A158805 A158806 A158807

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Mar 27 2009

STATUS

approved

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Last modified June 18 07:25 EDT 2021. Contains 345098 sequences. (Running on oeis4.)