

A071141


Numbers n such that sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n is neither a prime, nor a true power of prime and n is squarefree. Squarefree solutions of A071140.


4



30, 70, 286, 646, 1798, 3135, 3526, 3570, 6279, 7198, 8855, 8970, 10366, 10626, 10695, 11571, 15015, 16095, 16530, 17255, 17391, 20615, 20706, 20735, 20806, 23326, 24738, 24882, 26691, 28083, 31031, 36519, 36890, 38086, 38130, 41151, 41615, 44330, 44998
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OFFSET

1,1


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000


FORMULA

A008472(n)/A006530(n) is integer, n has at least 3 distinct prime factors and n is squarefree.


EXAMPLE

n = 286 = 2*11*13 has a form of 2pq, where p and q are twin primes;
n = 5414430 = 2*3*5*7*19*23*59, sum = 2+3+5+7+19+23+59 = 118 = 2*59.


MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w1], {w, 1, lf[x]}] sb[x_] := Apply[Plus, ba[x]] ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] amo[x_] := Abs[MoebiusMu[x]] Do[s=sb[n]/ma[n]; If[IntegerQ[s]&&Greater[lf[n], 1]&& !Equal[amo[n], 1], Print[{n, ba[n]}]], {n, 2, 1000000}]
(* Second program: *)
Select[Range@ 45000, Function[n, And[Length@ # > 1, SquareFreeQ@ n, Divisible[Total@ #, Last@ #]] &[FactorInteger[n][[All, 1]] ]]] (* Michael De Vlieger, Jul 18 2017 *)


CROSSREFS

Cf. A008472, A006530, A000961, A025475, A037074, A071139A071147.
Sequence in context: A295102 A131647 A301900 * A071312 A071142 A218327
Adjacent sequences: A071138 A071139 A071140 * A071142 A071143 A071144


KEYWORD

nonn


AUTHOR

Labos Elemer, May 13 2002


STATUS

approved



