A169666 Numbers divisible by the sum of 5th powers of their digits.
1, 10, 100, 110, 111, 1000, 1010, 1011, 1100, 1101, 1110, 1122, 1232, 2112, 2210, 4100, 4150, 4151, 4224, 10000, 10010, 10011, 10100, 10101, 10110, 11000, 11001, 11010, 11022, 11100, 11122, 11220, 12012, 12110, 12210, 12320, 14550, 20000, 21120, 21321, 22100
Offset: 1
Examples
21321 is a term since 2^5 + 1^5 + 3^5 + 2^5 + 1^5 = 309 and 21321 = 69*309. 54748 is a term since 5^5 + 4^5 + 7^5 + 4^5 + 8^5 = 54748.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Digit.
Programs
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Maple
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:
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Mathematica
Select[Range[10^4], Divisible[#, Plus @@ (IntegerDigits[#]^5)] &] (* Amiram Eldar, Jan 31 2021 *)
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PARI
is_A169666(n)=!(n%sum(i=1,#n=Vecsmall(Str(n)),(n[i]-48)^5))
Formula
A055014(a(n)) | a(n).
Extensions
Corrected and edited by D. S. McNeil, Nov 20 2010
More terms from Amiram Eldar, Jan 31 2021