The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A305565

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Regular triangle where T(n,k) is the number of finite sets of positive integers with least common multiple n and greatest common divisor k.
(history; published version)

#6 by Susanna Cuyler at Tue Jun 05 22:36:08 EDT 2018

STATUS

proposed

approved

#5 by Gus Wiseman at Tue Jun 05 11:06:47 EDT 2018

STATUS

editing

proposed

#4 by Gus Wiseman at Tue Jun 05 07:52:30 EDT 2018

CROSSREFS

Cf. A076078, A181819, A281116, A285572, A290103, A304818, A305563, A305564, A305566, A305567.

KEYWORD

nonn,changed,tabl

#3 by Gus Wiseman at Tue Jun 05 07:36:07 EDT 2018

EXAMPLE

The T(12,2) = 7 sets are {2,12}, {4,6}, {2,4,6}, {2,4,12}, {2,6,12}, {4,6,12}, {2,4,6,12}.

#2 by Gus Wiseman at Tue Jun 05 07:35:44 EDT 2018

NAME

allocated for Gus WisemanRegular triangle where T(n,k) is the number of finite sets of positive integers with least common multiple n and greatest common divisor k.

DATA

1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 0, 1, 7, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 4, 2, 0, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 1, 7, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 32, 7, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0

OFFSET

1,7

FORMULA

If k divides n then T(n,k) = T(n/k,1) = A305564(n/k); otherwise T(n,k) = 0.

EXAMPLE

Triangle begins:

1

1 1

1 0 1

2 1 0 1

1 0 0 0 1

7 1 1 0 0 1

1 0 0 0 0 0 1

4 2 0 1 0 0 0 1

2 0 1 0 0 0 0 0 1

7 1 0 0 1 0 0 0 0 1

1 0 0 0 0 0 0 0 0 0 1

32 7 2 1 0 1 0 0 0 0 0 1

The T(12,2) = 7 sets are {2,12}, {4,6}, {2,4,6}, {2,4,12}, {2,6,12}, {4,6,12}, {2,4,6,12}.

MATHEMATICA

Table[Length[Select[Subsets[Divisors[n]], And[GCD@@#==k, LCM@@#==n]&]], {n, 20}, {k, n}]

CROSSREFS

Cf. A076078, A181819, A281116, A285572, A290103, A304818, A305563, A305564.

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, Jun 05 2018

STATUS

approved

editing

#1 by Gus Wiseman at Tue Jun 05 07:35:44 EDT 2018

NAME

allocated for Gus Wiseman

KEYWORD

allocated

STATUS

approved