A135105 Digital sum (base the n-th prime) of n^5.

1, 4, 11, 16, 15, 12, 23, 44, 45, 40, 41, 72, 93, 98, 99, 48, 133, 108, 109, 160, 117, 172, 81, 120, 217, 176, 159, 102, 221, 144, 187, 262, 169, 304, 375, 276, 241, 158, 211, 316, 273, 72, 313, 320, 397, 406, 227, 582, 335, 236, 187, 460, 293, 274, 663, 178, 433, 538

Offset: 1

Author

Hieronymus Fischer, Dec 24 2007

Keywords

• nonn
• base

Examples

			a(2) = ds_prime(2)(2^5) = ds_3(32) = 1+0+1+2 = 4;
a(6) = ds_prime(5)(5^5) = ds_11(3125) = 2+9+3+1 = 15.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

Table[Total[IntegerDigits[n^5,Prime[n]]],{n,60}] (* Harvey P. Dale, Jul 19 2013  *)

PARI

a(n) = vecsum(digits(n^5, prime(n))); \\ Michel Marcus, Sep 24 2016

Formula

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

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