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A089352
Numbers that are divisible by the sum of their distinct prime factors (A008472).
11
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
KEYWORD
easy,nonn
AUTHOR
Ramin Naimi (rnaimi(AT)oxy.edu), Dec 26 2003
EXTENSIONS
Name edited by Michel Marcus, Jul 15 2020
STATUS
approved