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A260523 Numbers n such that (sum of digits of n) + (product of digits of n) is semiprime.

%I A260523 #10 Aug 29 2015 01:02:13
%S A260523 2,3,5,7,14,17,24,28,33,38,39,40,41,42,46,47,49,55,60,64,67,68,69,71,
%T A260523 74,76,82,83,86,90,93,94,96,103,105,108,109,111,112,114,116,121,122,
%U A260523 124,126,130,141,142,144,146,150,161,162,164,166,180,190,202,204,207
%N A260523 Numbers n such that (sum of digits of n) + (product of digits of n) is semiprime.
%H A260523 K. D. Bajpai, <a href="/A260523/b260523.txt">Table of n, a(n) for n = 1..10000</a>
%e A260523 a(6) = 17. (1+7) + (1*7) = 8 + 7 = 15 = 3 * 5, which is semiprime.
%e A260523 a(10) = 38. (3+8) + (3*8) = 11 + 24 = 35 = 5 * 7, which is semiprime.
%p A260523 with(numtheory):A260523 := proc() local a; a:= (add(d,d=convert(n, base, 10)) + mul(d,d=convert(n, base, 10))  ); if bigomega(a)=2 then RETURN (n); fi; end: seq(A260523 (),n=1..300);
%t A260523 Select[Range[1000], PrimeOmega[(Plus@@IntegerDigits[#]) + (Times@@IntegerDigits[#])] == 2 &]
%o A260523 (PARI) for(n=1,500,d=digits(n);s=sumdigits(n);p=prod(i=1,#d,d[i]);if(bigomega(s+p)==2,print1(n,", "))) \\ _Derek Orr_, Aug 27 2015
%Y A260523 Cf. A001358, A007953, A007954, A061762, A214629.
%K A260523 nonn,base,easy
%O A260523 1,1
%A A260523 _K. D. Bajpai_, Jul 28 2015