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 A047968 a(n) = Sum_{d|n} p(d), where p(d) = A000041 = number of partitions of d. 52
 1, 3, 4, 8, 8, 17, 16, 30, 34, 52, 57, 99, 102, 153, 187, 261, 298, 432, 491, 684, 811, 1061, 1256, 1696, 1966, 2540, 3044, 3876, 4566, 5846, 6843, 8610, 10203, 12610, 14906, 18491, 21638, 26508, 31290, 38044, 44584, 54133, 63262, 76241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Inverse Moebius transform of A000041. Row sums of triangle A137587. - Gary W. Adamson, Jan 27 2008 Row sums of triangle A168021. - Omar E. Pol, Nov 20 2009 Row sums of triangle A168017. Row sums of triangle A168018. - Omar E. Pol, Nov 25 2009 Sum of the partition numbers of the divisors of n. - Omar E. Pol, Feb 25 2014 Conjecture: for n > 6, a(n) is strictly increasing. - Franklin T. Adams-Watters, Apr 19 2014 Number of constant multiset partitions of multisets spanning an initial interval of positive integers with multiplicities an integer partition of n. - Gus Wiseman, Sep 16 2018 LINKS T. D. Noe, Table of n, a(n) for n=1..1000 N. J. A. Sloane, Transforms FORMULA G.f.: Sum_{k>0} (-1+1/Product_{i>0} (1-z^(k*i))). - Vladeta Jovovic, Jun 22 2003 G.f.: sum(n>0,A000041(n)*x^n/(1-x^n)). - Mircea Merca, Feb 24 2014. a(n) = A168111(n) + A000041(n). - Omar E. Pol, Feb 26 2014 a(n) = Sum_{y is a partition of n} A000005(GCD(y)). - Gus Wiseman, Sep 16 2018 EXAMPLE For n = 10 the divisors of 10 are 1, 2, 5, 10, hence the partition numbers of the divisors of 10 are 1, 2, 7, 42, so a(10) = 1 + 2 + 7 + 42 = 52. - Omar E. Pol, Feb 26 2014 From Gus Wiseman, Sep 16 2018: (Start) The a(6) = 17 constant multiset partitions:   (111111)  (111)(111)    (11)(11)(11)  (1)(1)(1)(1)(1)(1)   (111222)  (12)(12)(12)   (111122)  (112)(112)   (112233)  (123)(123)   (111112)   (111123)   (111223)   (111234)   (112234)   (112345)   (123456) (End) MAPLE with(combinat): with(numtheory): a := proc(n) c := 0: l := sort(convert(divisors(n), list)): for i from 1 to nops(l) do c := c+numbpart(l[i]) od: RETURN(c): end: for j from 1 to 60 do printf(`%d, `, a(j)) od: # Zerinvary Lajos, Apr 14 2007 MATHEMATICA a[n_] := Sum[ PartitionsP[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 44}] (* Jean-François Alcover, Oct 03 2013 *) CROSSREFS Cf. A000041, A000837, A047966, A055893, A137587, A003606 (Euler transform). Cf. A002033, A003238, A018783, A034729, A052409, A078392, A100953, A319162. Sequence in context: A002246 A310016 A030014 * A322117 A181778 A245026 Adjacent sequences:  A047965 A047966 A047967 * A047969 A047970 A047971 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 11 1999 STATUS approved

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Last modified May 30 08:04 EDT 2020. Contains 334712 sequences. (Running on oeis4.)