A053869 Sum of divisors of n less than n is even.

1, 6, 9, 10, 12, 14, 20, 22, 24, 25, 26, 28, 30, 34, 38, 40, 42, 44, 46, 48, 49, 52, 54, 56, 58, 60, 62, 66, 68, 70, 74, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 121, 122, 124, 126, 130, 132, 134, 136, 138, 140

Offset: 1

Author

Henry Bottomley, Mar 29 2000

Keywords

• nonn
• easy

Comments

Numbers which if odd are squares and which if even are neither squares nor twice squares.

Numbers whose sum of proper divisors is even. - Omar E. Pol, Aug 14 2009

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A001065, A028982, A053868.

Programs

Haskell

a053869 n = a053869_list !! (n-1)
a053869_list = filter (even . a001065) [1..]
-- Reinhard Zumkeller, Nov 01 2015, Sep 15 2011
a053869_list = map (+ 1) $ findIndices even $ map a001065 [1..]
-- Reinhard Zumkeller, Sep 15 2011

PARI

is(n)=if(n%2,issquare(n), !issquare(n) && !issquare(n/2)) \\ Charles R Greathouse IV, Sep 27 2015

Formula

a(n) = 2n + 2*sqrt(n) + O(1). - Charles R Greathouse IV, Sep 27 2015

Extensions

Offset fixed by Reinhard Zumkeller, Sep 15 2011