A070308 "Canada perfect numbers": n such that the sum of digits^2 of n equals the sum of d|n, 1

125, 581, 8549, 16999

Offset: 1

Author

Benoit Cloitre, May 12 2002

Keywords

• nonn
• base
• easy
• fini
• full

Comments

Those numbers were defined by J. Fabrykowski, B. Wolk and R. Padmanabhan (University of Manitoba) for the 125th anniversary of Canada.

There are no further terms. - David Wasserman, May 13 2003

Examples

			125 is a term because 1^2 + 2^2 + 5^2 = 30 = 5 + 25.
		

References

• 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.

Programs

Maple

select(t -> add(x^2, x=convert(t,base,10)) = numtheory:-sigma(t) - 1 - t, [$1..20000]); # Robert Israel, Apr 07 2016

Mathematica

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 *)

PARI

isok(n) = my(d=digits(n)); sum(k=1, #d, d[k]^2) == sigma(n) - n - 1; \\ Michel Marcus, Apr 07 2016