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A126028
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Perfect square roots: numbers such that (SOPF(n)*d(n))^2 = sigma(n) where SOPF(n) =sum of prime factors of n, d(n) = number of divisors of n, sigma(n) = sum of divisors of n.
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1
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22446139, 26116291, 28097023, 30236557, 31090489, 31124341, 49941589, 61137673, 62224039, 66960589, 71334867, 71585139, 82266591, 83045869, 92346023, 92837591, 105183961, 114762567, 123563821, 130399138, 131494219
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Mersenne Forum, Perfect roots
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EXAMPLE
| n = 22446139 factors as 31*67*101*107. SOPF(n) = 31+67+101+107 = 306, d(n) = 2^4 = 16, sigma(n) = (31+1)*(67+1)*(101+1)*(107+1) = 23970816, (SOPF(n)*d(n))^2 = (306*16)^2 = 23970816 = sigma(n).
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CROSSREFS
| Subsequence of A006532. Cf. A126029, A008472, A000005, A000203.
Sequence in context: A069317 A022211 A046397 * A069377 A204414 A114666
Adjacent sequences: A126025 A126026 A126027 * A126029 A126030 A126031
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KEYWORD
| nonn
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AUTHOR
| Fred Schneider (frederick.william.schneider(AT)gmail.com), Dec 14 2006
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EXTENSIONS
| Clarified and extended by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 11 2009
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