

A178981


2^A003418(n); for n >= 1, the least number > 1 that can be expressed simultaneously as a kth power of some integer for all 1 <= k <= n.


2




OFFSET

0,1


COMMENTS

Equivalently, for n >= 1, the least number > 1 of objects that can be arranged as a kcube (kdimensional hypercube) for all 1 <= k <= n.
a(7) = 2^420 contains 127 decimal digits.
From Jianing Song, Jul 20 2021: (Start)
Let F_q be the finite field with q elements, then F_a(n) is the smallest extension field of F_2 such that every polynomial of degree at most n splits into linear factors.
Union_{n>=0} F_a(n) is the algebraic clousre of F_2, which is the unique algebraically closed field with characteristic 2 and transcendence degree 0 (note that an algebraically closed field is uniquely determined by its characteristic and transcendence degree). Union_{n>=0} F_(2^(n!)) = Union_{n>=0} F_A050923(n) gives the same field.
Obviously, here 2 can be replaced by any prime p provided that {a(n)} is defined as a(n) = p^A003418(n). (End)


LINKS

Jianing Song, Table of n, a(n) for n = 0..10
Index to divisibility sequences


EXAMPLE

a(6) = 2^A003418(6) = 2^60 = 1152921504606846976 [= (2^60)^1] = (2^30)^2 = 1073741824^2 = (2^20)^3 = 1048576^3 = (2^15)^4 = 32768^4 = (2^12)^5 = 4096^5 = (2^10)^6 = 1024^6, while no smaller integer > 1 can be expressed simultaneously as a square, cube, 4th, 5th, and 6th power of integers.


PROG

(PARI) a(n)=2^(lcm(vector(n, i, i))) \\ Jianing Song, Jul 20 2021, following a PARI program for A003418


CROSSREFS

Cf. A003418, A050923.
Sequence in context: A295580 A177956 A345758 * A050923 A326960 A067700
Adjacent sequences: A178978 A178979 A178980 * A178982 A178983 A178984


KEYWORD

nonn,easy,changed


AUTHOR

Rick L. Shepherd, Jan 02 2011


STATUS

approved



