A055014 Sum of 5th powers of digits of n.

0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 1, 2, 33, 244, 1025, 3126, 7777, 16808, 32769, 59050, 32, 33, 64, 275, 1056, 3157, 7808, 16839, 32800, 59081, 243, 244, 275, 486, 1267, 3368, 8019, 17050, 33011, 59292, 1024, 1025, 1056, 1267, 2048

Offset: 0

Author

Henry Bottomley, May 31 2000

Keywords

• base
• nonn

Comments

Fixed points are listed in A052464. - M. F. Hasler, Apr 12 2015

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• K. Chikawa, K. Iséki, T. Kusakabe, and K. Shibamura, Computation of cyclic parts of Steinhaus problem for power 5, Acta Arithmetica 7 (1962), 253-254. [From _Don Knuth_, Sep 07 2015]
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A003132, A055012, A055013.

Cf. A007953, A055017, A076313, A076314.

Cf. A052464.

Programs

Magma

[0] cat [&+[d^5: d in Intseq(n)]: n in [1..45]]; // Bruno Berselli, Feb 01 2013

Maple

A055014 := proc(n)
   add(d^5,d=convert(n,base,10)) ;
end proc: # R. J. Mathar, Jul 08 2012

Mathematica

Total/@(IntegerDigits[Range[50]]^5)  (* Harvey P. Dale, Jan 22 2011 *)
Table[Sum[DigitCount[n][[i]] i^5, {i, 9}], {n, 0, 45}] (* Bruno Berselli, Feb 01 2013 *)

PARI

A055014(n)=sum(i=1, #n=digits(n), n[i]^5) \\ M. F. Hasler, Apr 12 2015

Formula

a(n) = Sum_{k>=1} (floor(n/10^k) - 10*floor(n/10^(k+1)))^5. - Hieronymus Fischer, Jun 25 2007

a(10n+k) = a(n) + k^5, 0 <= k < 10. - Hieronymus Fischer, Jun 25 2007