A135103 Digital sum (base the n-th prime) of n^3.

1, 4, 3, 4, 5, 12, 7, 26, 25, 20, 41, 36, 37, 56, 63, 40, 41, 72, 61, 90, 117, 118, 113, 96, 73, 76, 99, 116, 89, 120, 181, 138, 169, 112, 251, 156, 109, 116, 57, 188, 35, 108, 87, 128, 181, 118, 83, 258, 129, 284, 179, 188, 317, 214, 231, 338, 273, 442, 311, 400, 253

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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

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

Example

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.

Mathematica

Table[Total[IntegerDigits[n^3, Prime[n]]], {n, 70}] (* Harvey P. Dale, Oct 21 2011 *)

Crossrefs

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

Sequence in context: A260031 A132293 A205398 * A369052 A282822 A193694

Adjacent sequences: A135100 A135101 A135102 * A135104 A135105 A135106

Keyword

nonn,base

Author

Hieronymus Fischer, Dec 24 2007

Status

approved