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A063893 Numbers k such that the sum of proper divisors or aliquot parts of k^2 is a square. 0
1, 3, 49, 35713, 102851, 949818597, 1070640001, 74145779101, 138452510557, 158236686397, 640606652893, 2814821518321, 9081196437853, 36236716613821, 97748813502577, 185178952282141, 433755354387133 (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
747834604942753, 1543596825805057, 2356096433066461, 6853335405451201 and 7704992936528497 are also terms. - Martin Ehrenstein, Jul 30 2023
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.
LINKS
EXAMPLE
49 is a term 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)), print1(n, ", ")))
CROSSREFS
Sequence in context: A180602 A326342 A203700 * A291707 A145572 A309869
KEYWORD
nonn,nice,hard,more
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
a(11)-a(17) from Martin Ehrenstein, Jul 30 2023
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)