A063893 Numbers k such that the sum of proper divisors or aliquot parts of k^2 is a square.

1, 3, 49, 35713, 102851, 949818597, 1070640001, 74145779101, 138452510557, 158236686397, 640606652893, 2814821518321, 9081196437853, 36236716613821, 97748813502577, 185178952282141, 433755354387133

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

Table of n, a(n) for n=1..17.

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

Cf. A008847, A001065, A065764.

Sequence in context: A180602 A326342 A203700 * A291707 A145572 A309869

Adjacent sequences: A063890 A063891 A063892 * A063894 A063895 A063896

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