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 A018818 Number of partitions of n into divisors of n. 51
 1, 2, 2, 4, 2, 8, 2, 10, 5, 11, 2, 45, 2, 14, 14, 36, 2, 81, 2, 92, 18, 20, 2, 458, 7, 23, 23, 156, 2, 742, 2, 202, 26, 29, 26, 2234, 2, 32, 30, 1370, 2, 1654, 2, 337, 286, 38, 2, 9676, 9, 407, 38, 454, 2, 3132, 38, 3065, 42, 47, 2, 73155, 2, 50, 493, 1828, 44, 5257, 2, 740, 50, 5066 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Reinhard Zumkeller, Dec 11 2009: (Start) For odd primes p: a(p^2) = p + 2; for n > 1: a(A001248(n)) = A052147(n); for odd primes p > 3: a(3*p) = 2*p + 4; for n > 2: a(A001748(n)) = A100484(n) + 4. (End) LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (the first 1000 terms were computed by T. D. Noe) Douglas Bowman et al., Problem 6640: Partitions of n into parts which are divisors of n, American Mathematical Monthly 99:3 (1992), pp. 276-277. Hansraj Gupta, Partitions of n into divisors of m, Indian J. Pure Appl. Math. 6:11 (1975), pp. 1276-1286. Martin Klazar, What is an answer? — remarks, results and problems on PIO formulas in combinatorial enumeration, part I, arXiv:1808.08449 [math.CO], 2018. Rémy Sigrist, Colored logarithmic scatterplot of the first 10000 terms (where the color is function of A000005(n)) FORMULA Coefficient of x^n in expansion of 1/Product_{d divides n} (1-x^d). - Vladeta Jovovic, Sep 28 2002 a(n) = 2 iff n is prime. - Juhani Heino, Aug 27 2009 a(n) = f(n,n,1) where f(n,m,k) = f(n,m,k+1) + f(n,m-k,k)*0^(n mod k) if k <= m, otherwise 0^m. - Reinhard Zumkeller, Dec 11 2009 Paul Erdős, Andrew M. Odlyzko, and the Editors of the AMM give bounds; see Bowman et al. - Charles R Greathouse IV, Dec 04 2012 EXAMPLE The a(6) = 8 representations of 6 are 6 = 3 + 3 = 3 + 2 + 1 = 3 + 1 + 1 + 1 = 2 + 2 + 2 = 2 + 2 + 1 + 1 = 2 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1. MAPLE A018818 := proc(n)     local a, p, w, el ;     a := 0 ;     for p in combinat[partition](n) do         w := true ;         for el in p do             if modp(n, el) <> 0 then                 w := false;                 break;             end if;         end do:         if w then             a := a+1 ;         end if;     end do:     a ; end proc: # R. J. Mathar, Mar 30 2017 MATHEMATICA Table[d = Divisors[n]; Coefficient[Series[1/Product[1 - x^d[[i]], {i, Length[d]}], {x, 0, n}], x, n], {n, 100}] (* T. D. Noe, Jul 28 2011 *) PROG (Haskell) a018818 n = p (init \$ a027750_row n) n + 1 where    p _      0 = 1    p []     _ = 0    p ks'@(k:ks) m | m < k     = 0                   | otherwise = p ks' (m - k) + p ks m -- Reinhard Zumkeller, Apr 02 2012 (PARI) a(n)=numbpartUsing(n, divisors(n)); numbpartUsing(n, v, mx=#v)=if(n<1, return(n==0)); sum(i=1, mx, numbpartUsing(n-v[i], v, i)) \\ inefficient; Charles R Greathouse IV, Jun 21 2017 (MAGMA) [#RestrictedPartitions(n, {d:d in Divisors(n)}): n in [1..100]]; // Marius A. Burtea, Jan 02 2019 CROSSREFS Cf. A002577, A033630, A171565, A211110, A027750, A210442, A225244, A161148 (partitions in squared divisors). Sequence in context: A072478 A190014 A100577 * A157019 A067538 A305982 Adjacent sequences:  A018815 A018816 A018817 * A018819 A018820 A018821 KEYWORD nonn,nice,look AUTHOR STATUS approved

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Last modified September 21 04:59 EDT 2019. Contains 327253 sequences. (Running on oeis4.)