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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A032741, A091954.

Sequence in context: A093641 A209638 A191844 * A066522 A193159 A308018

Adjacent sequences: A096154 A096155 A096156 * A096158 A096159 A096160

Keyword

nonn

Author

Reinhard Zumkeller, Jun 18 2004

Status

approved