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Numbers n such that sum of digits (A007953) is a divisor of sum of prime divisors (A008472).
9

%I #13 Sep 08 2022 08:45:07

%S 2,3,5,7,10,42,70,84,91,100,104,110,114,115,130,143,148,154,160,170,

%T 182,185,212,215,221,222,228,230,234,238,250,266,295,304,312,326,336,

%U 372,402,412,425,437,460,468,485,494,516,555,558,583,700,702,721,730

%N Numbers n such that sum of digits (A007953) is a divisor of sum of prime divisors (A008472).

%H Harvey P. Dale, <a href="/A075657/b075657.txt">Table of n, a(n) for n = 1..1000</a>

%e digsum(10) = 1 + 0 = 1, PrimeDivisors(10) = PrimeDivisors(2 *5) = {2,5} and sopf(10) = 2 + 5 = 7 = 7*1.

%e digsum(154) = 1 + 5 + 4 = 10, PrimeDivisors(154) = PrimeDivisors(2 * 7 * 11) = {2,7,11} and sopf(154) = 2+7+11 = 20 = 2*10.

%t Select[Range[2,800],Divisible[Total[Select[Divisors[#],PrimeQ]], Total[ IntegerDigits[#]]]&] (* _Harvey P. Dale_, Sep 23 2012 *)

%o (Magma) [m:m in [2..730]| &+PrimeDivisors(m) mod &+Intseq(m) eq 0]; // _Marius A. Burtea_, Jul 11 2019

%K nonn,base

%O 1,1

%A _Floor van Lamoen_, Sep 23 2002 and Sep 30 2002