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A066446 Number of unordered divisor pairs of n. 8
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

COMMENTS

a(n) = 1 iff n is a prime.

a(n) = A184389(n) - A000005(n) = A035116(n) - A184389(n). - Reinhard Zumkeller, Sep 08 2015

LINKS

Harry J. Smith, Table of n, a(n) for n=1,...,1000

FORMULA

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 C( d(n), 2) = d(n)*{ d(n)-1 }/2 which is a triangular number (A000217).

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) ) } [From 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

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Last modified February 22 05:58 EST 2018. Contains 299430 sequences. (Running on oeis4.)