A070308 - OEIS

%I #40 Feb 27 2024 03:00:05

%S 125,581,8549,16999

%N "Canada perfect numbers": n such that the sum of digits^2 of n equals the sum of d|n, 1<d<n.

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

%C There are no further terms. - _David Wasserman_, May 13 2003

%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 125, p. 43, Ellipses, Paris 2008.

%D Jean-Marie De Koninck and Armel Mercier, Introduction à la théorie des nombres, Collection Universitaire de Mathématiques, Modulo, p. 85.

%D J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique Des Nombres, Problem 700 pp. 91; 299, Ellipses Paris 2004.

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

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

%t 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 *)

%o (PARI) isok(n) = my(d=digits(n)); sum(k=1, #d, d[k]^2) == sigma(n) - n - 1; \\ _Michel Marcus_, Apr 07 2016

%K nonn,base,easy,fini,full

%O 1,1

%A _Benoit Cloitre_, May 12 2002