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A055014 Sum of 5th powers of digits of n.

%I A055014 #35 Sep 08 2022 08:45:01
%S A055014 0,1,32,243,1024,3125,7776,16807,32768,59049,1,2,33,244,1025,3126,
%T A055014 7777,16808,32769,59050,32,33,64,275,1056,3157,7808,16839,32800,59081,
%U A055014 243,244,275,486,1267,3368,8019,17050,33011,59292,1024,1025,1056,1267,2048
%N A055014 Sum of 5th powers of digits of n.
%C A055014 Fixed points are listed in A052464. - _M. F. Hasler_, Apr 12 2015
%H A055014 Seiichi Manyama, <a href="/A055014/b055014.txt">Table of n, a(n) for n = 0..10000</a>
%H A055014 K. Chikawa, K. Iséki, T. Kusakabe, and K. Shibamura, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa7/aa734.pdf">Computation of cyclic parts of Steinhaus problem for power 5</a>, Acta Arithmetica 7 (1962), 253-254. [From _Don Knuth_, Sep 07 2015]
%H A055014 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F A055014 a(n) = Sum_{k>=1} (floor(n/10^k) - 10*floor(n/10^(k+1)))^5. - _Hieronymus Fischer_, Jun 25 2007
%F A055014 a(10n+k) = a(n) + k^5, 0 <= k < 10. - _Hieronymus Fischer_, Jun 25 2007
%p A055014 A055014 := proc(n)
%p A055014    add(d^5,d=convert(n,base,10)) ;
%p A055014 end proc: # _R. J. Mathar_, Jul 08 2012
%t A055014 Total/@(IntegerDigits[Range[50]]^5)  (* _Harvey P. Dale_, Jan 22 2011 *)
%t A055014 Table[Sum[DigitCount[n][[i]] i^5, {i, 9}], {n, 0, 45}] (* _Bruno Berselli_, Feb 01 2013 *)
%o A055014 (Magma) [0] cat [&+[d^5: d in Intseq(n)]: n in [1..45]]; // _Bruno Berselli_, Feb 01 2013
%o A055014 (PARI) A055014(n)=sum(i=1, #n=digits(n), n[i]^5) \\ _M. F. Hasler_, Apr 12 2015
%Y A055014 Cf. A003132, A055012, A055013.
%Y A055014 Cf. A007953, A055017, A076313, A076314.
%Y A055014 Cf. A052464.
%K A055014 base,nonn
%O A055014 0,3
%A A055014 _Henry Bottomley_, May 31 2000