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A070308 "Canada perfect numbers": n such that the sum of digits^2 of n equals the sum of d|n, 1<d<n. 4
125, 581, 8549, 16999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Curiously, the arithmetic derivatives of 581, 8549 and 16999 are equal to the sum of their digits^2 and to the sum of d|n, 1<d<n. - Paolo P. Lava, Apr 07 2016

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.

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

Sequence in context: A067974 A034290 A295025 * A211176 A045170 A235896

Adjacent sequences:  A070305 A070306 A070307 * A070309 A070310 A070311

KEYWORD

nonn,base,easy,fini,full

AUTHOR

Benoit Cloitre, May 12 2002

STATUS

approved

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Last modified March 1 03:32 EST 2021. Contains 341732 sequences. (Running on oeis4.)