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A063893
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Numbers k such that the sum of proper divisors or aliquot parts of k^2 is a square.
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0
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1, 3, 49, 35713, 102851, 949818597, 1070640001, 74145779101, 138452510557, 158236686397, 640606652893, 2814821518321, 9081196437853, 36236716613821, 97748813502577, 185178952282141, 433755354387133
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.
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LINKS
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EXAMPLE
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49 is a term because 49^2 = 2401 and sum of aliquot divisors of 2401: 1+7+49+343 = 400 = 20^2.
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PROG
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(PARI) s(n)=sigma(n)-n;
for(n=1, 10^8, if(issquare(s(n^2)), print1(n, ", ")))
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CROSSREFS
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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