A171976 - OEIS

A171976

Numbers n such that the sum of the squares of the digits of n^n is a square.

0, 1, 2, 8, 10, 100, 123, 209, 312, 1000, 1668, 2191, 2268, 4767, 9338, 10000, 11004, 12248, 12322, 15926, 17951, 18202, 19764, 21807, 29509, 42647, 43072, 44750, 54237, 56634, 70383, 74032, 85325, 90906, 95261, 100000

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..36.

FORMULA

{n: A003132(n^n) in A000290}.

{n: n^n in A175396.}

EXAMPLE

8 is in the sequence because 8^8 = 16777216 and 1^2+6^2+7^2+7^2+7^2+2^2+1^2+6^2

= 225 = 15^2.

MAPLE

with(numtheory): digits:=200:nn:=5000:for n from 0 to nn do:l:=length(n^n):n0:=n^n:s:=0:for

m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+u^2:od:if sqrt(s)=

floor(sqrt(s))then printf(`%d, `, n):else fi:od:

MATHEMATICA

Join[{0}, Select[Range[100000], IntegerQ[Sqrt[Total[IntegerDigits[ #^#]^2]]]&]] (* Harvey P. Dale, Sep 25 2018 *)

PROG

(PARI) isok(n) = my(d = digits(n^n)); issquare (sum(i=1, #d, d[i]^2)); \\ Michel Marcus, Jan 15 2014

CROSSREFS

Sequence in context: A230826 A071184 A174153 * A362278 A081231 A229128

Adjacent sequences: A171973 A171974 A171975 * A171977 A171978 A171979

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Nov 19 2010

EXTENSIONS

Edited by D. S. McNeil, Nov 19 2010

Offset corrected and more terms added, Michel Marcus, Jan 15 2014

STATUS

approved