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

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Digit.

Formula

A055014(a(n)) | a(n).

Example

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.

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:

Mathematica

Select[Range[10^4], Divisible[#, Plus @@ (IntegerDigits[#]^5)] &] (* Amiram Eldar, Jan 31 2021 *)

Prog

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

Crossrefs

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

Sequence in context: A034088 A169664 A174417 * A169662 A124252 A121030

Adjacent sequences: A169663 A169664 A169665 * A169667 A169668 A169669

Keyword

nonn,base

Author

Michel Lagneau, Apr 05 2010

Extensions

Corrected and edited by D. S. McNeil, Nov 20 2010

More terms from Amiram Eldar, Jan 31 2021

Status

approved