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A063893 Numbers n such that sum of proper divisors or aliquot parts of n^2 is a square. 0
1, 3, 49, 35713, 102851, 949818597, 1070640001, 74145779101, 138452510557, 158236686397 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers 640606652893, 2814821518321, 9081196437853, 36236716613821 and 97748813502577 are also terms. - Donovan Johnson, Mar 31 2012

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

a(3) = 49 because 49^2 = 2401 and sum of aliquot divisors of 2401: 1+7+49+343 = 400 = 20^2.

PROG

(PARI) s(n)=sigma(n)-n; for(n=1, 10^8, if(issquare(s(n^2)), print(n)))

CROSSREFS

Cf. A008847, A001065.

Sequence in context: A180602 A326342 A203700 * A291707 A145572 A309869

Adjacent sequences:  A063890 A063891 A063892 * A063894 A063895 A063896

KEYWORD

hard,nice,nonn

AUTHOR

Jason Earls, Aug 29 2001

EXTENSIONS

a(6) from Naohiro Nomoto, Jun 06 2002

a(7) from Giovanni Resta, Jan 31 2012

a(8)-a(10) from Donovan Johnson, Mar 15 2012

STATUS

approved

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Last modified April 18 14:32 EDT 2021. Contains 343088 sequences. (Running on oeis4.)