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 A168111 Sum of the partition numbers of the proper divisors of n, with a(1) = 0. 2
 0, 1, 1, 3, 1, 6, 1, 8, 4, 10, 1, 22, 1, 18, 11, 30, 1, 47, 1, 57, 19, 59, 1, 121, 8, 104, 34, 158, 1, 242, 1, 261, 60, 300, 23, 514, 1, 493, 105, 706, 1, 959, 1, 1066, 217, 1258, 1, 1927, 16, 2010, 301, 2545, 1, 3442, 64, 3898, 494, 4568, 1, 6555, 1, 6845, 841, 8610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums of triangle A168021 except the first column. Row sums of triangle A168016 except the last column. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A047968(n) - A000041(n). G.f.: sum(n > 0, A000041(n)*x^(2*n)/(1-x^n). - Mircea Merca, Feb 24 2014 G.f.: x^2 + x^3 + 3*x^4 + x^5 + 6*x^6 + x^7 + 8*x^8 + 4*x^9 + 10*x^10 + x^11 + ... - Michael Somos, Feb 24 2014 MAPLE A047968 := proc(n) add(combinat[numbpart](d), d= numtheory[divisors](n) ) ; end proc: A000041 := proc(n) combinat[numbpart](n) ; end proc: A168111 := proc(n) A047968(n)-A000041(n) ; end proc: seq(A168111(n), n=1..90) ; # R. J. Mathar, Jan 25 2010 MATHEMATICA a[ n_] := If[n < 1, 0, Sum[ PartitionsP[ d] Boole[ d < n], {d, Divisors @ n}]]; (* Michael Somos, Feb 24 2014 *) PROG (PARI) A168111(n) = sumdiv(n, d, (d

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Last modified August 19 04:27 EDT 2019. Contains 326109 sequences. (Running on oeis4.)