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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.
4
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
1,1
LINKS
Mersenne Forum, Perfect roots
EXAMPLE
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).
CROSSREFS
KEYWORD
nonn
AUTHOR
Fred Schneider, Dec 14 2006
EXTENSIONS
Clarified and extended by Charles R Greathouse IV, Oct 11 2009
Clarified by Donovan Johnson, Jun 09 2013
STATUS
approved