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A168111
Sum of the partition numbers of the proper divisors of n, with a(1) = 0.
5
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
OFFSET
1,4
COMMENTS
Row sums of triangle A168021 except the first column.
Row sums of triangle A168016 except the last column.
LINKS
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<n)*numbpart(d)); \\ Antti Karttunen, Nov 14 2017
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Nov 22 2009
EXTENSIONS
Terms beyond a(12) from R. J. Mathar, Jan 25 2010
New name from Omar E. Pol, Feb 25 2014
STATUS
approved