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A245021 Semiprimes whose digit sum is a perfect cube.

%I A245021 #14 Apr 07 2017 12:39:08
%S A245021 10,26,35,62,134,143,161,206,215,305,314,323,341,413,422,611,1007,
%T A245021 1043,1115,1133,1142,1205,1214,1241,1313,1322,1403,1502,2033,2042,
%U A245021 2051,2105,2123,2231,2321,2402,2501,3005,3113,3131,3401,4022,4031,4103,4121,5102,5111
%N A245021 Semiprimes whose digit sum is a perfect cube.
%C A245021 Semiprimes in  A059094.
%C A245021 No a(n) have digit sum 27, because numbers with digit sum divisible by 9 are divisible by 9 and thus not semiprimes.  The first member of the sequence with digit sum > 8 is 28999999 = a(1006). - _Robert Israel_, Jul 10 2014
%H A245021 K. D. Bajpai, <a href="/A245021/b245021.txt">Table of n, a(n) for n = 1..1000</a>
%e A245021 35 is in the sequence because 35 = 5 * 7 which is semiprime. Also, (3 + 5) = 8 = 2^3.
%e A245021 1043 is in the sequence because 1043 = 7 * 149 which is semiprime. Also, (1 + 0 + 4 + 3) = 8 = 2^3.
%p A245021 N:= 10000: # to get all terms up to N
%p A245021 maxj:= floor((9*(1+ilog10(N)))^(1/3)):
%p A245021 cubes:= {seq(j^3,j=1..maxj)}:
%p A245021 filter:= proc(n)
%p A245021 local s;
%p A245021 if numtheory:-bigomega(n) <> 2 then return false fi;
%p A245021 s:= convert(convert(n,base,10),`+`);
%p A245021 member(s,cubes);
%p A245021 end proc:
%p A245021 select(filter, [$1..N]); # _Robert Israel_, Jul 10 2014
%t A245021 sppcQ[n_]:=PrimeOmega[n]==2&&IntegerQ[Surd[Total[IntegerDigits[n]],3]]; Select[Range[5200],sppcQ] (* _Harvey P. Dale_, Apr 07 2017 *)
%Y A245021 Cf. A001358,  A007953, A059094.
%K A245021 nonn,base
%O A245021 1,1
%A A245021 _K. D. Bajpai_, Jul 09 2014