

A076444


Smallest powerful number (definition 1) such that a(n)+n is also powerful.


4



8, 25, 1, 4, 4, 214369, 1, 1, 16, 2187, 16, 4, 36, 30459361, 1, 9, 8, 9, 8, 16, 4, 27, 4, 1, 100, 1, 9, 4, 196, 6859, 1, 4, 16, 899236854927, 1, 36, 27, 1331, 25, 9, 8, 518436000625, 200, 64, 4, 243, 25, 1, 32, 625, 49, 144, 72, 27, 9, 8, 64, 109503, 49, 4, 64, 3025, 1, 8, 16
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OFFSET

1,1


COMMENTS

McDaniel proved that a(n) exists for all n > 0.
Sister sequence of a(n)+n given by A103952.
a(110) > 10^22.  Donovan Johnson, Nov 19 2011


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B16


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..109
Wayne L. McDaniel, Representations of every integer as the difference of powerful numbers, Fibonacci Quarterly 20 (1982), pp. 8587.
Eric Weisstein's World of Mathematics, Powerful numbers


EXAMPLE

214369=463^2 and 214375=5^4*7^3 are the smallest pair of powerful numbers differing by 6, so a(6)=214369.


CROSSREFS

Cf. A001694, A103952, A103953, A103954.
Sequence in context: A132586 A208400 A103953 * A023056 A103954 A217012
Adjacent sequences: A076441 A076442 A076443 * A076445 A076446 A076447


KEYWORD

nonn


AUTHOR

Jud McCranie, Oct 13 2002


EXTENSIONS

More terms from Max Alekseyev, Feb 22 2005


STATUS

approved



