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

2, 3, 5, 7, 14, 17, 24, 28, 33, 38, 39, 40, 41, 42, 46, 47, 49, 55, 60, 64, 67, 68, 69, 71, 74, 76, 82, 83, 86, 90, 93, 94, 96, 103, 105, 108, 109, 111, 112, 114, 116, 121, 122, 124, 126, 130, 141, 142, 144, 146, 150, 161, 162, 164, 166, 180, 190, 202, 204, 207

Offset: 1

Author

K. D. Bajpai, Jul 28 2015

Keywords

• nonn
• base
• easy

Examples

			a(6) = 17. (1+7) + (1*7) = 8 + 7 = 15 = 3 * 5, which is semiprime.
a(10) = 38. (3+8) + (3*8) = 11 + 24 = 35 = 5 * 7, which is semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A007953, A007954, A061762, A214629.

Programs

Maple

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);

Mathematica

Select[Range[1000], PrimeOmega[(Plus@@IntegerDigits[#]) + (Times@@IntegerDigits[#])] == 2 &]

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