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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Abs(A032741(n) - 2*A091954(n)) <= 1.

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

EXAMPLE

Proper divisors of n=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

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

Adjacent sequences:  A096154 A096155 A096156 * A096158 A096159 A096160

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 18 2004

STATUS

approved

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)