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 A167934 a(n) = A000041(n) - A032741(n). 6
 1, 1, 1, 2, 3, 6, 8, 14, 19, 28, 39, 55, 72, 100, 132, 173, 227, 296, 380, 489, 622, 789, 999, 1254, 1568, 1956, 2433, 3007, 3713, 4564, 5597, 6841, 8344, 10140, 12307, 14880, 17969, 21636, 26012, 31182, 37331, 44582, 53167, 63260, 75170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) is also the number of partitions of n whose parts are not all equal, (including however the partition with a single part of size n). Note that the number of partitions of n whose parts are all equal gives the number of divisors of n, for n>0. (See also A144300.) LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A000041(n) - A032741(n). EXAMPLE The partitions of n = 6 are: 6 ....................... All parts are equal, but included .. (1). 5 + 1 ................... All parts are not equal ............ (2). 4 + 2 ................... All parts are not equal ............ (3). 4 + 1 + 1 ............... All parts are not equal ............ (4). 3 + 3 ................... All parts are equal, not included. 3 + 2 + 1 ............... All parts are not equal ............ (5). 3 + 1 + 1 + 1 ........... All parts are not equal ............ (6). 2 + 2 + 2 ............... All parts are equal, not included. 2 + 2 + 1 + 1 ........... All parts are not equal ............ (7). 2 + 1 + 1 + 1 + 1 ....... All parts are not equal ............ (8). 1 + 1 + 1 + 1 + 1 + 1 ... All parts are equal, not included. Then a(6) = 8. MAPLE b:= proc(n, i, k) option remember;       if n<0 then 0     elif n=0 then `if`(k=0, 1, 0)     elif i=0 then 0     else b(n, i-1, k)+          b(n-i, i, `if`(k<0, i, `if`(k<>i, 0, k)))       fi     end: a:= n-> 1 +b(n, n-1, -1): seq(a(n), n=0..50);  #  Alois P. Heinz, Dec 01 2010 MATHEMATICA a[0] = 1; a[n_] := PartitionsP[n] - DivisorSigma[0, n] + 1; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jan 08 2016 *) CROSSREFS Cf. A000005, A000009, A000041, A000065, A032741, A047967, A111133, A144300, A135010, A138121, A167930, A167932, A167935. Sequence in context: A326635 A212214 A089426 * A327690 A182269 A321360 Adjacent sequences:  A167931 A167932 A167933 * A167935 A167936 A167937 KEYWORD nonn AUTHOR Omar E. Pol, Nov 16 2009 EXTENSIONS More terms from Alois P. Heinz, Dec 01 2010 STATUS approved

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Last modified May 26 04:39 EDT 2022. Contains 354074 sequences. (Running on oeis4.)