cp's OEIS Frontend

A233482 Numbers for which the number of divisors and the sum of the distinct prime divisors are both perfect.

%I A233482 #10 Aug 11 2021 15:30:30
%S A233482 575,2057,2645,3179,4416,8512,12275,33534,94272,138431,203075,218176,
%T A233482 392747,715878,918592,982157,991841,1082176,1205405,1244387,1559616,
%U A233482 1690432,1966912,2344079,2464576,2982976,3386176,3452992,3625792,3821632,3867712,3900497
%N A233482 Numbers for which the number of divisors and the sum of the distinct prime divisors are both perfect.
%C A233482 Numbers n such that A000005(n) and A008472(n) are in the sequence A000396. See the sequence A081357 for the sublime numbers.
%H A233482 Donovan Johnson, <a href="/A233482/b233482.txt">Table of n, a(n) for n = 1..333</a> (terms < 10^11)
%e A233482 575 is in the sequence because tau(575) = 6 and sopf(575) = 28,
%e A233482 4416 is in the sequence because tau(4416) = 28 and sopf(4416) = 28,
%e A233482 12275 is in the sequence because tau(12275) = 6 and sopf(12275) = 496,
%e A233482 203075 is in the sequence because tau(203075) = 6 and sopf(203075) = 8128.
%p A233482 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 A233482 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 tau(n)=lst[p] then jj:=1:else fi:od:if ii=1 and jj=1 then printf(`%d, `,n):else fi:od:
%t A233482 Select[Range[4*10^6],AllTrue[{DivisorSigma[0,#],Total[FactorInteger[#][[All,1]]]},PerfectNumberQ]&] (* _Harvey P. Dale_, Aug 11 2021 *)
%Y A233482 Cf A000005, A000396, A081357, A008472.
%K A233482 nonn
%O A233482 1,1
%A A233482 _Michel Lagneau_, Dec 11 2013