A055015 Sum of 6th powers of digits of n.

0, 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1, 2, 65, 730, 4097, 15626, 46657, 117650, 262145, 531442, 64, 65, 128, 793, 4160, 15689, 46720, 117713, 262208, 531505, 729, 730, 793, 1458, 4825, 16354, 47385, 118378, 262873

Offset: 0

Author

Henry Bottomley, May 31 2000

Keywords

• base
• nonn

Comments

The only fixed points (n = 0, 1 and 548834) are listed in row 6 of A252648. - M. F. Hasler, Apr 12 2015

Links

• Michel Marcus, Table of n, a(n) for n = 0..999
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A003132.

Cf. A003132, A055012, A055013, A005514.

Cf. A007953, A055017, A076313, A076314.

Programs

Magma

[0] cat [&+[d^6: d in Intseq(n)]: n in [1..40]]; // Bruno Berselli, Feb 01 2013

Maple

for n from 0 to 3 do seq(n^6+j^6, j=0..9 ); od; # Zerinvary Lajos, Nov 06 2006

Mathematica

Table[Sum[DigitCount[n][[i]] i^6, {i, 9}], {n, 0, 40}] (* Bruno Berselli, Feb 01 2013 *)

PARI

A055015(n)=sum(i=1,#n=digits(n),n[i]^6) \\ M. F. Hasler, Apr 12 2015

Formula

a(n) = Sum_{k>0} (floor(n/10^k) - 10*floor(n/10^(k+1)))^6. - Hieronymus Fischer, Jun 25 2007

a(10n+k) = a(n) + k^6, 0 <= k < 10. - Hieronymus Fischer, Jun 25 2007