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A070308
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"Canada perfect numbers": n such that the sum of digits^2 of n equals the sum of d|n, 1<d<n.
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4
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OFFSET
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1,1
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COMMENTS
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Those numbers were defined by J. Fabrykowski, B. Wolk and R. Padmanabhan (University of Manitoba) for the 125th anniversary of Canada.
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 125, p. 43, Ellipses, Paris 2008.
Jean-Marie De Koninck and Armel Mercier, Introduction à la théorie des nombres, Collection Universitaire de Mathématiques, Modulo, p. 85.
J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique Des Nombres, Problem 700 pp. 91; 299, Ellipses Paris 2004.
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LINKS
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EXAMPLE
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125 is a term because 1^2 + 2^2 + 5^2 = 30 = 5 + 25.
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MAPLE
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select(t -> add(x^2, x=convert(t, base, 10)) = numtheory:-sigma(t) - 1 - t, [$1..20000]); # Robert Israel, Apr 07 2016
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MATHEMATICA
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cnQ[n_]:=Module[{sod=Total[Rest[Most[Divisors[n]]]]}, sod == Total[IntegerDigits[n]^2]]; Select[Range[2, 17000], cnQ] (* Harvey P. Dale, Jun 17 2011 *)
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PROG
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(PARI) isok(n) = my(d=digits(n)); sum(k=1, #d, d[k]^2) == sigma(n) - n - 1; \\ Michel Marcus, Apr 07 2016
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CROSSREFS
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KEYWORD
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nonn,base,easy,fini,full
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AUTHOR
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STATUS
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approved
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