

A233410


a(n) = smallest multiple m of n such that there are at most m/n perfect powers <= m.


1



1, 2, 3, 20, 45, 60, 77, 96, 117, 180, 209, 276, 312, 378, 420, 464, 510, 594, 646, 700, 756, 814, 874, 936, 1050, 1118, 1188, 1260, 1363, 1440, 1519, 1632, 1716, 1836, 1925, 2016, 2183, 2394, 2496, 2600, 2788, 2898, 3010, 3124, 3330
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OFFSET

1,2


COMMENTS

A perfect power is a prime power p^e with e != 1 (see A001597).
No value of the sequence belongs to A001597 except the first value 1.


REFERENCES

New Scientist, Enigma 1777, November 2013, submitted by Susan Denham.


LINKS

Martin Y. Champel, Table of n, a(n) for n = 1..9999


EXAMPLE

n=1: a(1)=1 as the only perfect power <= 1 is 1.
n=2: a(2)=2 as the only perfect power <= 2 is 1, and 2=2*1.
n=3: a(3)=3 as the only perfect power <= 3 is 1, and 3=3*1.
n=4: a(4)=20 as (1,4,8,9,16) are 5 perfect powers smaller than 20 and 20 = 4*5.
n=5: a(5)=45 as (1,4,8,9,16,25,27,32,36) are 9 perfect powers smaller than 45 and 45 = 5*9.


PROG

(Python)
a = A001597 'list of ordered perfect powers' = [1, 4, 8, 9, 16, 25, 27, 32, 36, ...]
A233410 = {}
n = 1
k = 1
while True
....while n * k >= a[k]:
........k += 1
....A233410[n] = n * k
....n += 1


CROSSREFS

Cf. A001597 = list of perfect powers, A069623 = number of perfect powers <= n
Sequence in context: A195686 A295365 A072472 * A318765 A055814 A151370
Adjacent sequences: A233407 A233408 A233409 * A233411 A233412 A233413


KEYWORD

nonn


AUTHOR

Martin Y. Champel, Dec 09 2013


STATUS

approved



