A135103 - OEIS

%I #7 Nov 21 2013 12:49:08

%S 1,4,3,4,5,12,7,26,25,20,41,36,37,56,63,40,41,72,61,90,117,118,113,96,

%T 73,76,99,116,89,120,181,138,169,112,251,156,109,116,57,188,35,108,87,

%U 128,181,118,83,258,129,284,179,188,317,214,231,338,273,442,311,400,253

%N Digital sum (base the n-th prime) of n^3.

%H Harvey P. Dale, <a href="/A135103/b135103.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)=ds_prime(n)(n^3), where ds_prime(n)=digital sum base the n-th prime.

%F a(n)=n^3-(prime(n)-1)*sum{k>0, floor(n^3/prime(n)^k)}.

%e a(2)=ds_prime(2)(2^3)=ds_3(8)=2+2=4; a(6)=ds_prime(6)(6^3)=ds_13(216)=1+3+8=12.

%t Table[Total[IntegerDigits[n^3,Prime[n]]],{n,70}] (* _Harvey P. Dale_, Oct 21 2011 *)

%Y Cf. A000040, A007953, A054899, A075771, A131451, A133620, A133900, A134599.

%K nonn,base

%O 1,2

%A _Hieronymus Fischer_, Dec 24 2007