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 A033630 Number of partitions of n into distinct divisors of n. 40
 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 8, 1, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 4, 1, 3, 1, 1, 1, 35, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 2, 1, 7, 1, 1, 1, 26, 1, 1, 1, 2, 1, 24, 1, 1, 1, 1, 1, 22, 1, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..10000 (1000 terms from T. D. Noe) FORMULA a(A005100(n)) = 1; a(A005835(n)) > 1. - Reinhard Zumkeller, Mar 02 2007 a(n) = f(n, n, 1) with f(n, m, k) = if k <= m then f(n, m, k + 1) + f(n, m - k, k + 1)*0^(n mod k) else 0^m. - Reinhard Zumkeller, Dec 11 2009 a(n) = [x^n] Product_{d|n} (1 + x^d). - Ilya Gutkovskiy, Jul 26 2017 a(n) = 1 if n is deficient (A005100) or weird (A006037). a(n) = 2 if n is perfect (A000396). - Alonso del Arte, Sep 24 2017 EXAMPLE a(12) = 3 because we have the partitions [12], [6, 4, 2], and [6, 3, 2, 1]. MAPLE with(numtheory): a:=proc(n) local div, g, gser: div:=divisors(n): g:=product(1+x^div[j], j=1..tau(n)): gser:=series(g, x=0, 105): coeff(gser, x^n): end: seq(a(n), n=1..100); # Emeric Deutsch, Mar 30 2006 # second Maple program: with(numtheory): a:= proc(n) local b, l; l:= sort([(divisors(n))[]]):       b:= proc(m, i) option remember; `if`(m=0, 1, `if`(i<1, 0,              b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i-1))))           end; forget(b):       b(n, nops(l))     end: seq(a(n), n=0..100); # Alois P. Heinz, Feb 05 2014 MATHEMATICA A033630 = Table[SeriesCoefficient[Series[Times@@((1 + z^#) & /@ Divisors[n]), {z, 0, n}], n ], {n, 512}] (* Wouter Meeussen *) A033630[n_] := f[n, n, 1]; f[n_, m_, k_] := f[n, m, k] = If[k <= m, f[n, m, k + 1] + f[n, m - k, k + 1] * Boole[Mod[n, k] == 0], Boole[m == 0]]; Array[A033630, 101, 0] (* Jean-François Alcover, Jul 29 2015, after Reinhard Zumkeller *) PROG (Haskell) a033630 0 = 1 a033630 n = p (a027750_row n) n where    p _  0 = 1    p [] _ = 0    p (d:ds) m = if d > m then 0 else p ds (m - d) + p ds m -- Reinhard Zumkeller, Feb 23 2014, Apr 04 2012, Oct 27 2011 CROSSREFS Cf. A018818. a(n) = A065205(n) + 1. Cf. A083206. - Reinhard Zumkeller, Jul 19 2010 Cf. A000009, A005153. Cf. A211111, A027750. Cf. A225245. Sequence in context: A292435 A069283 A285337 * A220122 A101446 A259396 Adjacent sequences:  A033627 A033628 A033629 * A033631 A033632 A033633 KEYWORD nonn AUTHOR EXTENSIONS More terms from Reinhard Zumkeller, Apr 21 2003 STATUS approved

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Last modified August 18 16:13 EDT 2018. Contains 313833 sequences. (Running on oeis4.)