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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.

%I A071141 #20 Jan 10 2025 10:08:36
%S A071141 30,70,286,646,1798,3135,3526,3570,6279,7198,8855,8970,10366,10626,
%T A071141 10695,11571,15015,16095,16530,17255,17391,20615,20706,20735,20806,
%U A071141 23326,24738,24882,26691,28083,31031,36519,36890,38086,38130,41151,41615,44330,44998
%N 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.
%H A071141 Donovan Johnson, <a href="/A071141/b071141.txt">Table of n, a(n) for n = 1..1000</a>
%F A071141 A008472(n)/A006530(n) is an integer, n has at least 3 distinct prime factors and n is squarefree.
%e A071141 n = 286 = 2*11*13 has a form of 2pq, where p and q are twin primes;
%e A071141 n = 5414430 = 2*3*5*7*19*23*59, sum = 2+3+5+7+19+23+59 = 118 = 2*59.
%t A071141 ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {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}]
%t A071141 (* Second program: *)
%t A071141 Select[Range@ 45000, Function[n, And[Length@ # > 1, SquareFreeQ@ n, Divisible[Total@ #, Last@ #]] &[FactorInteger[n][[All, 1]] ]]] (* _Michael De Vlieger_, Jul 18 2017 *)
%Y A071141 Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071147.
%K A071141 nonn
%O A071141 1,1
%A A071141 _Labos Elemer_, May 13 2002