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Digital sum (base the n-th prime) of n^5.
1

%I #13 Sep 24 2016 04:28:43

%S 1,4,11,16,15,12,23,44,45,40,41,72,93,98,99,48,133,108,109,160,117,

%T 172,81,120,217,176,159,102,221,144,187,262,169,304,375,276,241,158,

%U 211,316,273,72,313,320,397,406,227,582,335,236,187,460,293,274,663,178,433,538

%N Digital sum (base the n-th prime) of n^5.

%H G. C. Greubel, <a href="/A135105/b135105.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ds_prime(n)(n^5), where ds_prime(n) = digital sum base the n-th prime.

%F a(n) = n^5 - (prime(n)-1)*Sum_{k>0} ( floor(n^5/prime(n)^k) ).

%e a(2) = ds_prime(2)(2^5) = ds_3(32) = 1+0+1+2 = 4;

%e a(6) = ds_prime(5)(5^5) = ds_11(3125) = 2+9+3+1 = 15.

%t Table[Total[IntegerDigits[n^5,Prime[n]]],{n,60}] (* _Harvey P. Dale_, Jul 19 2013 *)

%o (PARI) a(n) = vecsum(digits(n^5, prime(n))); \\ _Michel Marcus_, Sep 24 2016

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

%K nonn,base

%O 1,2

%A _Hieronymus Fischer_, Dec 24 2007