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A096157 Numbers whose numbers of odd and even proper divisors differ at most by 1.

%I A096157 #18 Dec 16 2021 07:30:51
%S A096157 1,2,3,4,5,6,7,8,10,11,12,13,14,17,18,19,20,22,23,26,28,29,30,31,34,
%T A096157 37,38,41,42,43,44,46,47,50,52,53,54,58,59,61,62,66,67,68,70,71,73,74,
%U A096157 76,78,79,82,83,86,89,90,92,94,97,98,101,102,103,106,107,109,110,113
%N A096157 Numbers whose numbers of odd and even proper divisors differ at most by 1.
%C A096157 A union of 1, 4, primes, quadrupled primes, and all numbers of the form 4k+2. - _Ivan Neretin_, Aug 12 2015
%H A096157 Robert Israel, <a href="/A096157/b096157.txt">Table of n, a(n) for n = 1..10000</a>
%F A096157 Abs(A032741(a(n)) - 2*A091954(a(n))) <= 1.
%e A096157 Proper divisors of 42 are {1,2,3,6,7,14,21}: 4=#{1,3,7,21} are odd and 3=#{2,6,14} are even, as abs(4-3)=1, 42 is a term.
%p A096157 filter:= n -> if n::odd then isprime(n) elif n mod 4 = 0 then isprime(n/4) else true fi:
%p A096157 filter(1):= true: filter(4):= true:
%p A096157 select(filter, [$1..1000]); # _Robert Israel_, Aug 12 2015
%t A096157 okQ[n_] := With[{dd = Most[Divisors[n]]},
%t A096157      Abs[2 Count[dd, _?OddQ] - Length[dd]] <= 1];
%t A096157 Select[Range[1000], okQ] (* _Jean-François Alcover_, Dec 16 2021 *)
%o A096157 (PARI) is(n)=if(bittest(n,0),isprime(n),bittest(n,1)||isprime(n>>2))||n<9 \\ _M. F. Hasler_, Aug 13 2015
%Y A096157 Cf. A032741, A091954.
%K A096157 nonn
%O A096157 1,2
%A A096157 _Reinhard Zumkeller_, Jun 18 2004