A135104 Digital sum (base the n-th prime) of n^4.

1, 4, 5, 10, 15, 24, 17, 28, 27, 60, 31, 36, 81, 70, 71, 68, 117, 96, 37, 120, 81, 100, 139, 192, 97, 176, 123, 174, 205, 128, 193, 126, 137, 220, 201, 216, 133, 196, 397, 296, 189, 396, 321, 256, 305, 280, 331, 396, 445, 292, 313, 256, 481, 556, 417, 326, 553, 256

Offset: 1

Author

Hieronymus Fischer, Dec 24 2007

Keywords

• nonn
• base

Examples

			a(2) = ds_prime(2)(2^4) = ds_3(16) = 1+2+1 = 4;
a(6) = ds_prime(6)(6^4) = ds_13(1296) = 7+8+9 = 24.
		

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^4, Prime[n]]], {n, 50}] (* G. C. Greubel, Sep 23 2016 *)

PARI

a(n) = vecsum(digits(n^4, prime(n))); \\ Michel Marcus, Sep 24 2016

Formula

a(n) = ds_prime(n)(n^4), where ds_prime(n) = digital sum base the n-th prime.

a(n) = n^4 - (prime(n)-1)*Sum{k>0} ( floor(n^4/prime(n)^k) ).