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A066620 Number of decompositions of divisors of n into pairwise coprime triples. 2
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 7, 0, 0, 1, 1, 1, 4, 0, 1, 1, 3, 0, 7, 0, 2, 2, 1, 0, 4, 0, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 13, 0, 1, 2, 0, 1, 7, 0, 2, 1, 7, 0, 6, 0, 1, 2, 2, 1, 7, 0, 4, 0, 1, 0, 13, 1, 1, 1, 3, 0, 13, 1, 2, 1, 1, 1, 5, 0, 2, 2, 4, 0, 7, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

a(m) = a(n) if m and n have same factorization structure.

REFERENCES

Amarnath Murthy, Decomposition of the divisors of a natural number into pairwise coprime sets, Smarandache Notions Journal, vol. 12, No. 1-2-3, Spring 2001.pp 303-306.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

In the reference it is shown that if k is a squarefree number with r prime factors and m with (r+1) prime factors then a(m) = 4*a(k) + 2^k - 1.

a(n) = (tau(n^3)-3*tau(n)+2)/6. - Vladeta Jovovic, Nov 27 2004

EXAMPLE

a(24) = 3: the divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The decompositions are (1, 2, 3), (1, 2, 9), (1, 3, 4); a(30) = 7: the triples are (1, 2, 3), (1, 2, 5), (1, 3, 5), (2, 3, 5), (1, 3, 10), (1, 5, 6), (1, 2, 15).

PROG

(PARI) A066620(n) = (numdiv(n^3)-3*numdiv(n)+2)/6; \\ After Jovovic's formula. - Antti Karttunen, May 27 2017

(Python)

from sympy import divisor_count as d

def a(n): return (d(n**3) - 3*d(n) + 2)/6 # Indranil Ghosh, May 27 2017

CROSSREFS

Cf. A063647, A000005.

Sequence in context: A319058 A281116 A089233 * A219023 A025427 A245963

Adjacent sequences:  A066617 A066618 A066619 * A066621 A066622 A066623

KEYWORD

nonn

AUTHOR

K. B. Subramaniam (kb_subramaniambalu(AT)yahoo.com) and Amarnath Murthy, Dec 24 2001

EXTENSIONS

More terms from Vladeta Jovovic, Apr 03 2003

STATUS

approved

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Last modified June 24 17:58 EDT 2019. Contains 324330 sequences. (Running on oeis4.)