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%I #6 Dec 14 2013 02:15:33
%S 1104,1656,2128,2484,3726,4620,6930,7448,11550,12285,12696,16170,
%T 19044,20216,20475,23568,25410,26068,28566,28665,34125,35352,47775,
%U 53028,53235,54544,66885,70756,71875,79542,88725,91238,124215,146004,190904,192052,201180
%N Numbers for which the number of prime divisors counted with multiplicity and the sum of the distinct prime divisors are both perfect.
%C Numbers n such that A001222(n) and A008472(n) are in the sequence A000396.
%H Donovan Johnson, <a href="/A233563/b233563.txt">Table of n, a(n) for n = 1..1000</a>
%e 1104 is in the sequence because bigomega(1104) = 6 and sopf(1104) = 28,
%e 23568 is in the sequence because bigomega(23568) = 6 and sopf(23568) = 496,
%e 389904 is in the sequence because bigomega(389904) = 6 and sopf(389904) = 8128.
%p with(numtheory): lst:={6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216} :n1:=nops(lst): for n from 1 to 1000000 do :x:=factorset(n):n2:=nops(x): s:=sum('x[i]', 'i'=1..n2):
%p ii:=0:for m from 1 to n1 do:if s=lst[m] then ii:=1:else fi:od:jj:=0:for p from 1 to n1 do:if bigomega(n)=lst[p] then jj:=1:else fi:od:if ii=1 and jj=1 then printf(`%d, `, n):else fi:od:
%Y Cf. A000396, A081357, A008472, A001222, A233482.
%K nonn
%O 1,1
%A _Michel Lagneau_, Dec 13 2013
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