

A272242


a(n) is the least number c such that there are exactly n abchits with third member c, or 0 if no such c exists.


1



9, 81, 625, 729, 87808, 14641, 130321, 6561, 65536, 59049, 78125
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OFFSET

1,1


COMMENTS

An abchit is a triple of coprime positive integers a, b, c such that a + b = c and rad(abc) < c, where rad(n) is the largest squarefree number dividing n.
Conjecture: a(n) > 0 for all n.  Jianing Song, Sep 21 2018


LINKS

Table of n, a(n) for n=1..11.
Wikipedia, abc conjecture


EXAMPLE

a(2) = 81 because there are exactly 2 abchits ((1, 80, 81) and (32, 49, 81)) with third member 81 and count of abchits with fixed third member c isn't equal to 2 for every c < 81.


CROSSREFS

Cf. A272243.
Cf. A120498, A130510 (possible values of c in abchits).
Cf. A225426 (triples of abchits).
Cf. A130512 (radicals of abchits).
Cf. A007947 (radicals).
Sequence in context: A267961 A213297 A272243 * A206728 A206857 A073531
Adjacent sequences: A272239 A272240 A272241 * A272243 A272244 A272245


KEYWORD

nonn,hard,more


AUTHOR

Vladimir Letsko, Apr 23 2016


STATUS

approved



