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

1,1

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001358, A007953, A059094.

Sequence in context: A157075 A369668 A262998 * A045039 A322972 A080059

Adjacent sequences: A245018 A245019 A245020 * A245022 A245023 A245024

Keyword

nonn,base

Author

K. D. Bajpai, Jul 09 2014

Status

approved