login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089913 Table T(n,k) = lcm(n,k)/gcd(n,k) = n*k/gcd(n,k)^2 read by antidiagonals (n >= 1, k >= 1). 6
1, 2, 2, 3, 1, 3, 4, 6, 6, 4, 5, 2, 1, 2, 5, 6, 10, 12, 12, 10, 6, 7, 3, 15, 1, 15, 3, 7, 8, 14, 2, 20, 20, 2, 14, 8, 9, 4, 21, 6, 1, 6, 21, 4, 9, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 11, 5, 3, 2, 35, 1, 35, 2, 3, 5, 11, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12, 13, 6, 33, 10, 45 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A multiplicative analog of absolute difference A049581. Exponents in prime factorization of T(n,k) are absolute differences of those of n and k. Commutative non-associative operator with identity 1. T(nx,kx)=T(n,k), T(n^x,k^x)=T(n,k)^x, etc.

The bivariate function log(T(., .)) is a distance (or metric) function. It is a weighted analog of A130836, in the sense that if e_i (resp. f_i) denotes the exponent of prime p_i in the factorization of m (resp. of n), then both log(T(m, n)) and A130836(m, n) are writable as Sum_{i} w_i * abs(e_i - f_i). For A130836, w_i = 1 for all i, whereas for log(T(., .)), w_i = log(p_i). - Luc Rousseau, Sep 17 2018

If the analog of absolute difference, as described in the first comment, is determined by factorization into distinct terms of A050376 instead of by prime factorization, the equivalent operation is defined by A059897 and is associative. The positive integers form a group under A059897. The two factorization methods give the same factorization for squarefree numbers (A005117), so that T(.,.) restricted to A005117 is associative. Thus the squarefree numbers likewise form a group under the operation defined by this sequence. - Peter Munn, Apr 04 2019

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..5050

FORMULA

A130836(n, k) = A001222(T(n, k)). - Luc Rousseau, Sep 17 2018

EXAMPLE

T(6,10) = lcm(6,10)/gcd(6,10) = 30/2 = 15.

  1,  2,  3,  4,  5, ...

  2,  1,  6,  2, 10, ...

  3,  6,  1, 12, 15, ...

  4,  2, 12,  1, 20, ...

  5, 10, 15, 20,  1, ...

  ...

MATHEMATICA

Flatten[Table[LCM[i, m - i]/GCD[i, m - i], {m, 15}, {i, m - 1}]] (* Ivan Neretin, Apr 27 2015 *)

PROG

(GAP) T:=Flat(List([1..13], n->List([1..n-1], k->Lcm(k, n-k)/Gcd(k, n-k)))); # Muniru A Asiru, Oct 24 2018

(PARI) A089913(n, k)=n*k/gcd(n, k)^2 \\ M. F. Hasler, Dec 06 2019

CROSSREFS

Cf. A049581, A003990, A003991, A130836, A001222, A005117, A050376, A059897.

Sequence in context: A227287 A289236 A280172 * A257522 A059897 A325821

Adjacent sequences:  A089910 A089911 A089912 * A089914 A089915 A089916

KEYWORD

easy,nonn,tabl,changed

AUTHOR

Marc LeBrun, Nov 14 2003

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)