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A171976
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Numbers n such that the sum of the squares of the digits of n^n is a square.
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0
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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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listen;
history;
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internal format)
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..36.
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FORMULA
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{n: A003132(n^n) in A000290}.
{n: n^n in A175396.}
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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Join[{0}, Select[Range[100000], IntegerQ[Sqrt[Total[IntegerDigits[ #^#]^2]]]&]] (* Harvey P. Dale, Sep 25 2018 *)
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PROG
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(PARI) isok(n) = my(d = digits(n^n)); issquare (sum(i=1, #d, d[i]^2)); \\ Michel Marcus, Jan 15 2014
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CROSSREFS
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Sequence in context: A230826 A071184 A174153 * A081231 A229128 A121715
Adjacent sequences: A171973 A171974 A171975 * A171977 A171978 A171979
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KEYWORD
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nonn,base
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AUTHOR
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Michel Lagneau, Nov 19 2010
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EXTENSIONS
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Edited by D. S. McNeil, Nov 19 2010
Offset corrected and more terms added, Michel Marcus, Jan 15 2014
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STATUS
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approved
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