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%I #22 Jun 03 2023 10:09:56
%S 1,5,12,70,117,210,247,330,715,782,1080,1520,1926,2625,2752,3015,3290,
%T 3432,4510,5370,5922,6902,7740,8400,9560,11310,12105,13776,14652,
%U 15862,17442,21182,21540,23002,24130,26070,27270,30602,31032,32340,34580,38320,39285
%N Pentagonal numbers that are also Niven numbers.
%C Intersection of A000326 and A005349.
%H K. D. Bajpai, <a href="/A242043/b242043.txt">Table of n, a(n) for n = 1..10344</a>
%e a(3) = 12 = 3*(3 * 3 - 1)/2 is a pentagonal number. Since 12 is divisible by 1 + 2 = 3, it is also a Harshad number and therefore in the sequence.
%e a(5) = 117 = 9*(3 * 9 - 1)/2 is a pentagonal number. Since 117 is divisible by 1 + 1 + 7 = 9 is also a Harshad number, and therefore in the sequence.
%t A242043 = {}; Do[k = (3*n^2 - n)/2; If[IntegerQ[k/(Plus @@ IntegerDigits[k])], AppendTo[A242043, k]], {n, 300}]; A242043 (* Bajpai *)
%t Select[Table[n(3n - 1)/2, {n, 200}], Divisible[#, Plus@@IntegerDigits[#]] &] (* _Alonso del Arte_, Aug 16 2014 *)
%t Select[PolygonalNumber[5,Range[200]],Mod[#,Total[IntegerDigits[#]]]==0&] (* _Harvey P. Dale_, Nov 30 2022 *)
%Y Cf. A000326, A005349, A076713.
%K nonn,base
%O 1,2
%A _K. D. Bajpai_, Aug 12 2014