

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
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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(n1): 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



