cp's OEIS Frontend

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.

%I A126028 #8 Oct 02 2013 16:23:32
%S A126028 22446139,26116291,28097023,30236557,31090489,31124341,49941589,
%T A126028 61137673,62224039,66960589,71334867,71585139,82266591,83045869,
%U A126028 88658031,92346023,92837591,105183961,114762567,123563821,129616270,130399138,131494219,134156197
%N 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.
%H A126028 Donovan Johnson, <a href="/A126028/b126028.txt">Table of n, a(n) for n = 1..1000</a>
%H A126028 Mersenne Forum, <a href="http://www.mersenneforum.org/showthread.php?p=87743">Perfect roots</a>
%e A126028 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).
%Y A126028 Subsequence of A006532. Cf. A126029, A008472, A000005, A000203, A001414, A226479, A226480.
%K A126028 nonn
%O A126028 1,1
%A A126028 _Fred Schneider_, Dec 14 2006
%E A126028 Clarified and extended by _Charles R Greathouse IV_, Oct 11 2009
%E A126028 Clarified by _Donovan Johnson_, Jun 09 2013