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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A329947 Integers k such that the radical of the cumulative product of k^k/k! equals its predecessor. 1
1, 12, 30, 36, 40, 60, 70, 72, 96, 108, 112, 126, 150, 175, 180, 192, 198, 210, 224, 240, 270, 280, 306, 312, 324, 330, 336, 350, 351, 352, 378, 384, 396, 399, 400, 408, 418, 420, 432, 440, 441, 442, 448, 455, 456, 462, 475, 490, 494, 520, 539, 540, 546, 560 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

No prime numbers appear in this sequence.

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

Consider the rows 11 and 12 of Pascal's triangle.

P11 = [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1].

P12 = [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1].

lcm(P11) = 2310 and radical(2310) = 2310.

lcm(P12) = 27720 and radical(27720) = 2310.

Since radical(lcm(P11)) = radical(lcm(P12)) 12 is in this sequence.

Also: 1 is in this sequence because radical(lcm(P0)) = radical(lcm([1])) = radical(1) = 1 = radical(lcm([1, 1])) = radical(lcm(P1)).

MAPLE

h := n -> mul(k^k/factorial(k), k=0..n):

rad := n -> mul(k, k = numtheory[factorset](n)):

g := proc(n) option remember; rad(h(n)) end:

isA329947 := n -> g(n) = g(n-1): select(isA329947, [$1..560]);

CROSSREFS

Cf. A056606, A056077.

Sequence in context: A050689 A144565 A334587 * A115912 A083096 A307348

Adjacent sequences:  A329944 A329945 A329946 * A329948 A329949 A329950

KEYWORD

nonn

AUTHOR

Peter Luschny, Dec 21 2019

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 July 7 16:09 EDT 2020. Contains 335496 sequences. (Running on oeis4.)