A272242 a(n) is the least number c such that there are exactly n abc-hits with third member c, or 0 if no such c exists.

9, 81, 625, 729, 87808, 14641, 130321, 6561, 65536, 59049, 78125, 2476099, 2097152, 131072, 15625, 117649, 418195493, 1953125, 1048576, 7253758561, 844596301, 11962890625, 531441, 10510100501, 714924299, 33554432, 19487171, 8388608, 2073071593, 390625, 62523502209

Offset

1,1

Comments

An abc-hit 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..31.

Hugo Pfoertner, Table of n, a(n) for n=1..311, intentionally not provided as b-file due to unknown status of verification.

ABC@Home, Data collected so far, 2014.

Wikipedia, abc conjecture

Example

a(2) = 81 because there are exactly 2 abc-hits ((1, 80, 81) and (32, 49, 81)) with third member 81 and count of abc-hits 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 abc-hits).

Cf. A225426 (triples of abc-hits).

Cf. A130512 (radicals of abc-hits).

Cf. A007947 (radicals).

Cf. A395935.

Sequence in context: A267961 A213297 A272243 * A392045 A206728 A206857

Adjacent sequences: A272239 A272240 A272241 * A272243 A272244 A272245

Keyword

nonn

Author

Vladimir Letsko, Apr 23 2016

Extensions

More terms from Hugo Pfoertner using data from ABC@Home, May 09 2026

Status

approved