A169666 - OEIS

%I #22 Feb 16 2025 08:33:11

%S 1,10,100,110,111,1000,1010,1011,1100,1101,1110,1122,1232,2112,2210,

%T 4100,4150,4151,4224,10000,10010,10011,10100,10101,10110,11000,11001,

%U 11010,11022,11100,11122,11220,12012,12110,12210,12320,14550,20000,21120,21321,22100

%N Numbers divisible by the sum of 5th powers of their digits.

%H Amiram Eldar, <a href="/A169666/b169666.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Digit.html">Digit</a>.

%F A055014(a(n)) | a(n).

%e 21321 is a term since 2^5 + 1^5 + 3^5 + 2^5 + 1^5 = 309 and 21321 = 69*309.

%e 54748 is a term since 5^5 + 4^5 + 7^5 + 4^5 + 8^5 = 54748.

%p with(numtheory):for n from 1 to 200000 do:l:=evalf(floor(ilog10(n))+1): n0:=n:indic:=0:s5:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :s5:=s5+u^5: od:if irem(n,s5)=0 then print (n):else fi:od:

%t Select[Range[10^4], Divisible[#, Plus @@ (IntegerDigits[#]^5)] &] (* _Amiram Eldar_, Jan 31 2021 *)

%o (PARI) is_A169666(n)=!(n%sum(i=1,#n=Vecsmall(Str(n)),(n[i]-48)^5))

%Y Cf. A005349, A034087, A034088, A055014, A169665,

%K nonn,base,changed

%O 1,2

%A _Michel Lagneau_, Apr 05 2010

%E Corrected and edited by _D. S. McNeil_, Nov 20 2010

%E More terms from _Amiram Eldar_, Jan 31 2021