The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #12 Feb 06 2021 07:09:33
%S 0,1,5,6501,8400,10542,10795,18760,21540,32340,45850,50142,50692,
%T 55200,60501,72490,91390,104412,127750,160230,170185,179401,208507,
%U 239800,250717,272001,273280,333940,346801,400675,429070,442002,520087,536107,552370,602617,637330
%N Pentagonal numbers for which both the sum of the digits and the product of the digits are pentagonal numbers.
%H Amiram Eldar, <a href="/A117711/b117711.txt">Table of n, a(n) for n = 1..10000</a>
%e 6501 is a pentagonal number whose sum of digits 6+5+0+1 = 12 and product of digits 6*5*0*1 = 0 are both pentagonal.
%t sod[n_] := Plus @@ IntegerDigits[n]; pod[n_] := Times @@ IntegerDigits[n]; pentQ[n_] := n == 0 || IntegerQ[(Sqrt[24*n + 1] + 1)/6]; Select[Table[n*(3*n - 1)/2, {n, 0, 1000}], pentQ[sod[#]] && pentQ[pod[#]] &] (* _Amiram Eldar_, Feb 06 2021 *)
%Y Cf. A000326, A007953, A007954, A117053, A117064.
%K base,nonn
%O 1,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006
%E Offset and data corrected by _Amiram Eldar_, Feb 06 2021