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 A023645 a(n) = tau(n)-1 if n is odd or tau(n)-2 if n is even. 10
 0, 0, 1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 1, 2, 3, 3, 1, 4, 1, 4, 3, 2, 1, 6, 2, 2, 3, 4, 1, 6, 1, 4, 3, 2, 3, 7, 1, 2, 3, 6, 1, 6, 1, 4, 5, 2, 1, 8, 2, 4, 3, 4, 1, 6, 3, 6, 3, 2, 1, 10, 1, 2, 5, 5, 3, 6, 1, 4, 3, 6, 1, 10, 1, 2, 5, 4, 3, 6, 1, 8, 4, 2, 1, 10, 3, 2, 3, 6, 1, 10, 3, 4, 3, 2, 3, 10, 1, 4, 5, 7, 1, 6, 1, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Vertex-transitive graphs of valency 2 with n nodes. Number of values of k such that n+2 divided by k leaves a remainder 2. - Amarnath Murthy, Aug 01 2002 Number of divisors of n that are less than n/2. - Peter Munn, Mar 31 2017 For n > 2, a(n) is the number of planar arrangements of equal-sized regular n-gons such that their centers lie on a circle and neighboring n-gons have an edge in common. - Peter Munn, Apr 23 2017 Number of partitions of n into two distinct parts such that the smaller divides the larger. - Wesley Ivan Hurt, Dec 21 2017 REFERENCES CRC Handbook of Combinatorial Designs, 1996, p. 649. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Felix Fröhlich et al., Rings of regular polygons, SeqFan thread, March 26 2017. Gordon Royle, Transitive Graphs FORMULA G.f.: Sum_{k>0} x^(3*k) / (1 - x^k). - Michael Somos, Apr 29 2003. a(2*n) = A069930(n). a(2*n + 1) = A095374(n). - Michael Somos, Aug 30 2012 a(n) = A072528(n+2,2) for n > 2. - Peter Munn, May 14 2017 EXAMPLE x^3 + x^4 + x^5 + 2*x^6 + x^7 + 2*x^8 + 2*x^9 + 2*x^10 + x^11 + 4*x^12 + ... MAPLE with(numtheory); f := n->if n mod 2 = 1 then tau(n)-1 else tau(n)-2; fi; MATHEMATICA Table[s = DivisorSigma[0, n]; If[OddQ[n], s - 1, s - 2], {n, 100}] (* T. D. Noe, Nov 18 2013 *) Array[DivisorSigma[0, #] - 1 - Boole@ EvenQ@ # &, 104] (* Michael De Vlieger, Apr 25 2017 *) PROG (PARI) {a(n) = if( n<1, 0, numdiv(n) - 2 + n%2)} /* Michael Somos, Apr 29 2003 */ (PARI) a(n) = sumdiv(n, d, d < n/2); \\ Michel Marcus, Apr 01 2017 CROSSREFS Cf. A000005, A023637-A023647. Cf. A069930, A095374. Second column of A072528. Sequence in context: A158946 A303428 A223853 * A167865 A218654 A054571 Adjacent sequences:  A023642 A023643 A023644 * A023646 A023647 A023648 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Dec 03 2001 STATUS approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)