A245021 Semiprimes whose digit sum is a perfect cube.

10, 26, 35, 62, 134, 143, 161, 206, 215, 305, 314, 323, 341, 413, 422, 611, 1007, 1043, 1115, 1133, 1142, 1205, 1214, 1241, 1313, 1322, 1403, 1502, 2033, 2042, 2051, 2105, 2123, 2231, 2321, 2402, 2501, 3005, 3113, 3131, 3401, 4022, 4031, 4103, 4121, 5102, 5111

Offset: 1

Author

K. D. Bajpai, Jul 09 2014

Keywords

• nonn
• base

Comments

Semiprimes in A059094.

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

Examples

			35 is in the sequence because 35 = 5 * 7 which is semiprime. Also, (3 + 5) = 8 = 2^3.
1043 is in the sequence because 1043 = 7 * 149 which is semiprime. Also, (1 + 0 + 4 + 3) = 8 = 2^3.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A007953, A059094.

Programs

Maple

N:= 10000: # to get all terms up to N
maxj:= floor((9*(1+ilog10(N)))^(1/3)):
cubes:= {seq(j^3,j=1..maxj)}:
filter:= proc(n)
local s;
if numtheory:-bigomega(n) <> 2 then return false fi;
s:= convert(convert(n,base,10),`+`);
member(s,cubes);
end proc:
select(filter, [$1..N]); # Robert Israel, Jul 10 2014

Mathematica

sppcQ[n_]:=PrimeOmega[n]==2&&IntegerQ[Surd[Total[IntegerDigits[n]],3]]; Select[Range[5200],sppcQ] (* Harvey P. Dale, Apr 07 2017 *)