A226479
Numbers n such that (sopf(n)*d(n))^2 = sigma(n) where sopf(n) = sum of distinct prime factors of n (A008472) and d(n) = number of divisors of n.
Original entry on oeis.org
22446139, 26116291, 28097023, 30236557, 31090489, 31124341, 39618558, 41628195, 49941589, 51777957, 61137673, 62224039, 66960589, 71096795, 71334867, 71585139, 72304400, 82266591, 83045869, 92346023, 92837591, 105183961, 114762567, 117908994, 123563821
Offset: 1
n = 22446139 = 31*67*101*107. sopf(n) = 31+67+101+107 = 306. d(n) = 16. (sopf(n)*d(n))^2 = (306*16)^2 = 23970816 = sigma(n).
A226480
Squarefree numbers n such that (sopf(n)*d(n))^2 = sigma(n) where sopf(n) = sum of prime factors of n and d(n) = number of divisors of n.
Original entry on oeis.org
22446139, 26116291, 28097023, 30236557, 31090489, 31124341, 49941589, 61137673, 62224039, 66960589, 71334867, 71585139, 82266591, 83045869, 92346023, 92837591, 105183961, 114762567, 123563821, 130399138, 131494219, 134156197, 134867722, 135095767, 136026037
Offset: 1
n = 22446139 = 31*67*101*107. sopf(n) = 31+67+101+107 = 306. d(n) = 16. (sopf(n)*d(n))^2 = (306*16)^2 = 23970816 = sigma(n).
A126029
The smallest positive k such that ( sopfr(k)*tau(k) )^n = sigma(k) where sopfr is the sum of prime factors with multiplicity (A001414).
Original entry on oeis.org
35, 22446139, 4481106818619089
Offset: 1
22446139 factors as: 31*67*101*107=k, sopfr(k) = sum of prime factors of k = 31+67+101+107 = 306. tau(k) = num of divisors of k = 2^4 = 16. sigma(k) = sum of divisors of k = (31+1)*(67+1)*(101+1)*(107+1) = 23970816. (306*16)^2 = 23970816. As this k turns out to be minimal, a(2)=22446139.
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