A126028 Perfect square roots: numbers n such that (sopfr(n)*d(n))^2 = sigma(n) where sopfr = sum of prime factors with multiplicity (A001414), d(n) = number of divisors of n, sigma(n) = sum of divisors of n.

22446139, 26116291, 28097023, 30236557, 31090489, 31124341, 49941589, 61137673, 62224039, 66960589, 71334867, 71585139, 82266591, 83045869, 88658031, 92346023, 92837591, 105183961, 114762567, 123563821, 129616270, 130399138, 131494219, 134156197

Offset: 1

Author

Fred Schneider, Dec 14 2006

Keywords

• nonn

Examples

			n = 22446139 = 31*67*101*107. sopfr(n) = 31+67+101+107 = 306, d(n) = 2^4 = 16, sigma(n) = (31+1)*(67+1)*(101+1)*(107+1) = 23970816, (sopfr(n)*d(n))^2 = (306*16)^2 = 23970816 = sigma(n).
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• Mersenne Forum, Perfect roots

Crossrefs

Subsequence of A006532. Cf. A126029, A008472, A000005, A000203, A001414, A226479, A226480.

Extensions

Clarified and extended by Charles R Greathouse IV, Oct 11 2009

Clarified by Donovan Johnson, Jun 09 2013