A247199 Numbers n such that the sum of all terms of the form d/d' with d>d' both divisors of n is an integer.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 42, 43, 47, 49, 53, 54, 59, 61, 64, 66, 67, 71, 73, 78, 79, 81, 83, 89, 97, 101, 102, 103, 107, 109, 113, 114, 121, 125, 127, 128, 131, 135, 137, 138, 139, 147, 149, 151, 156, 157

Offset

1,2

Comments

A000961 (power of primes) is a subsequence, since for a prime power all divisors are divisible by all smaller divisors.

The list of numbers that are not prime powers begin: 42, 54, 66, 78, ...

Links

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

Example

Divisors of 27 are: 27, 9, 3, 1 and (27/9 + 27/3 + 27/1) + (9/3 + 9/1) + 3/1 = 54, an integer.
Divisors of 6 are: 6, 3, 2, 1 and (6/3 + 6/2 + 6/1) + (3/2 + 3/1) + 2/1 = 35/2 not an integer, so 6 is not here.

Prog

(PARI) isok(n) = {d = divisors(n); s = 0; forstep(k = #d-1, 1, -1, forstep(j=k-1, 1, -1, s += d[k]/d[j]; ); ); denominator(s) == 1; }
(Haskell)
import Data.List (tails); import Data.Ratio ((%), denominator)
a247199 n = a247199_list !! (n-1)
a247199_list = filter f [1..] where
   f x = 1 == denominator
         (sum [v % w | (v:ws) <- tails $ reverse $ a027750_row x, w <- ws])
-- Reinhard Zumkeller, Nov 25 2014

Crossrefs

Cf. A027750 (divisors of n), A000961 (prime powers).

Sequence in context: A325247 A306013 A268082 * A087441 A326645 A371445

Adjacent sequences: A247196 A247197 A247198 * A247200 A247201 A247202

Keyword

nonn

Author

Michel Marcus, Nov 25 2014

Status

approved