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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 (list; graph; refs; listen; history; text; internal format)
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. 85-87.

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

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)