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

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

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

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

Sequence in context: A331358 A046397 A226479 * A226480 A238154 A069377

Adjacent sequences: A126025 A126026 A126027 * A126029 A126030 A126031

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