The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A066446 Number of unordered divisor pairs of n. 11
 0, 1, 1, 3, 1, 6, 1, 6, 3, 6, 1, 15, 1, 6, 6, 10, 1, 15, 1, 15, 6, 6, 1, 28, 3, 6, 6, 15, 1, 28, 1, 15, 6, 6, 6, 36, 1, 6, 6, 28, 1, 28, 1, 15, 15, 6, 1, 45, 3, 15, 6, 15, 1, 28, 6, 28, 6, 6, 1, 66, 1, 6, 15, 21, 6, 28, 1, 15, 6, 28, 1, 66, 1, 6, 15, 15, 6, 28, 1, 45, 10, 6, 1, 66, 6, 6, 6, 28 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..1000 from Harry J. Smith) FORMULA a(p) = 1 iff p is a prime. Combinations of d(n), the number of divisors of n (A000005), taken two at a time. If the canonical factorization of n into prime powers is Product p^e(p) then d(n) = Product (e(p) + 1). Therefore a(n) = C(d(n), 2) = d(n)*{ d(n)-1 }/2 which is a triangular number (A000217). a(n) = A184389(n) - A000005(n) = A035116(n) - A184389(n). - Reinhard Zumkeller, Sep 08 2015 a(n) = A000217(A000005(n)-1). - Antti Karttunen, Sep 21 2018 a(n) = Sum_{k|n, i|n, i < k} 1. - Wesley Ivan Hurt, Aug 20 2020 EXAMPLE The divisors of 6 are 1, 2, 3 & 6. In unordered pairs they are {1, 2}, {1, 3}, {1, 6}, {2, 3}, {2, 6}, & {3, 6}. Since there are six pairs, a(6) = 6. Also d(6) = 4. 4*3/2 = 6. MATHEMATICA Table[ Binomial[ DivisorSigma[0, n], 2], {n, 1, 100}] PROG (PARI) { for (n=1, 1000, a=binomial(numdiv(n), 2); write("b066446.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 15 2010 (Haskell) a066446 = a000217 . subtract 1 . a000005' -- Reinhard Zumkeller, Sep 08 2015 CROSSREFS Cf. A000005, A000217, A129510. Cf. A035116, A184389. Sequence in context: A019570 A239303 A040011 * A069625 A111614 A193279 Adjacent sequences:  A066443 A066444 A066445 * A066447 A066448 A066449 KEYWORD easy,nonn AUTHOR Robert G. Wilson v, Dec 28 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 11 05:30 EDT 2021. Contains 342886 sequences. (Running on oeis4.)