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A096157
Numbers whose numbers of odd and even proper divisors differ at most by 1.
2
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, 37, 38, 41, 42, 43, 44, 46, 47, 50, 52, 53, 54, 58, 59, 61, 62, 66, 67, 68, 70, 71, 73, 74, 76, 78, 79, 82, 83, 86, 89, 90, 92, 94, 97, 98, 101, 102, 103, 106, 107, 109, 110, 113
OFFSET
1,2
COMMENTS
A union of 1, 4, primes, quadrupled primes, and all numbers of the form 4k+2. - Ivan Neretin, Aug 12 2015
LINKS
FORMULA
Abs(A032741(a(n)) - 2*A091954(a(n))) <= 1.
EXAMPLE
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.
MAPLE
filter:= n -> if n::odd then isprime(n) elif n mod 4 = 0 then isprime(n/4) else true fi:
filter(1):= true: filter(4):= true:
select(filter, [$1..1000]); # Robert Israel, Aug 12 2015
MATHEMATICA
okQ[n_] := With[{dd = Most[Divisors[n]]},
Abs[2 Count[dd, _?OddQ] - Length[dd]] <= 1];
Select[Range[1000], okQ] (* Jean-François Alcover, Dec 16 2021 *)
PROG
(PARI) is(n)=if(bittest(n, 0), isprime(n), bittest(n, 1)||isprime(n>>2))||n<9 \\ M. F. Hasler, Aug 13 2015
CROSSREFS
Sequence in context: A093641 A209638 A191844 * A066522 A193159 A308018
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 18 2004
STATUS
approved