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A261560 Semiprimes sp such that (sum of digits of (sp)) + (product of digits of (sp)) is also semiprime.

%I A261560 #14 Sep 08 2022 08:46:13
%S A261560 14,33,38,39,46,49,55,69,74,82,86,93,94,111,121,122,141,142,146,161,
%T A261560 166,202,214,221,226,247,249,254,259,262,274,278,287,295,301,303,323,
%U A261560 334,346,386,411,427,445,454,458,469,485,489,501,505,529,542,565,586,589
%N A261560 Semiprimes sp such that (sum of digits of (sp)) + (product of digits of (sp)) is also semiprime.
%H A261560 K. D. Bajpai, <a href="/A261560/b261560.txt">Table of n, a(n) for n = 1..10000</a>
%e A261560 a(1) = 14 = (2 * 7), is semiprime. (1+4) + (1*4) = 9 = (3 * 3) is also semiprime.
%e A261560 a(3) = 38 = (2 * 19), is semiprime. (3+8) + (3*8) = 35 = (7 * 5) is also semiprime.
%p A261560 with(numtheory): select(n -> bigomega(n)=2 and bigomega( add(d, d=convert(n, base, 10)) + mul(d, d=convert(n, base, 10)) ) = 2, [seq(n, n=1..300)]);
%t A261560 Select[Range[2000], PrimeOmega[#] == 2 && PrimeOmega[(Plus @@ IntegerDigits[#]) + (Times @@ IntegerDigits[#])] == 2 &]
%o A261560 (PARI) for(n = 1, 300, d = digits(n); pd = prod(i = 1, #d, d[i]); if(bigomega(n)==2 && bigomega(sumdigits(n) + pd)==2, print1(n,", ")));
%o A261560 (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [11..300] | IsSemiprime(n) and IsSemiprime(k) where k is (&+Intseq(n) + &*Intseq(n))];
%Y A261560 Cf. A001358, A061762, A118688, A118689, A118690.
%K A261560 nonn,base
%O A261560 1,1
%A A261560 _K. D. Bajpai_, Aug 24 2015