|
| |
|
|
A081512
|
|
a(n) = smallest number which can be expressed as the sum of n of its distinct divisors, or 0 if no such number exists.
|
|
4
| |
|
|
1, 0, 6, 12, 24, 24, 48, 60, 84, 120, 120, 120, 180, 180, 240, 360, 360, 360, 360, 672, 720, 720, 720, 840, 840, 1080, 1260, 1260, 1260, 1680, 1680, 1680, 2160, 2520, 2520, 2520, 2520, 2520, 2520, 3360, 4320, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| In the following triangle the n-th row contains the n divisors pertaining to the this sequence; a(n) = sum of the n-th row.
1
- -
1 2 3
1 2 3 6
1 2 3 6 12
1 2 3 4 6 8
1 2 3 6 8 12 16
|
|
|
EXAMPLE
| a(2) = 0. All other entries are nonzero.
24 is a sum of 6 of its divisors. Namely, 1+2+3+4+6+8=24. Furthermore, 24 is the smallest natural number with at least 6 divisors (not including itself), so it must be the smallest natural number that is a sum of 6 of its divisors.
|
|
|
MAPLE
| A081512 := proc(n) local a, dvs, dset, s, p; if n= 2 then RETURN(0) ; end if; for a from 1 do dvs := numtheory[divisors](a) ; dset := combinat[choose](dvs, n) ; for s in dset do if add(p, p=s) = a then RETURN(a) ; end if; end do; end do: end: for n from 2 do a := A081512(n) ; printf("%d, ", a) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 11 2008]
|
|
|
CROSSREFS
| Cf. A081513, A081514.
Sequence in context: A005694 A172079 * A096387 A094185 A074902 A096366
Adjacent sequences: A081509 A081510 A081511 * A081513 A081514 A081515
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 27 2003
|
|
|
EXTENSIONS
| Corrected by Caleb M. Shor (cshor(AT)bates.edu), Sep 26 2007
Extended beyond a(7) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 11 2008
a(16)-a(49) from Max Alekseyev (maxale(AT)gmail.com), Jul 27 2009
|
| |
|
|
