A330486 Earliest start of a run of n numbers divisible by a seventh power larger than one.

128, 76544, 2372890624, 390491792890623, 2083234733888734218749, 18962123650219836035505781245

Offset

1,1

Comments

In De Koninck's book, a(4) was probable but not certain. It also gives probable terms for a(5) and a(6).

From David A. Corneth, Dec 18 2019: (Start)

a(6) <= 18962123650219836035505781245

a(7) <= 105574810222799317012520534891328125

a(8) <= 352061173826332779662070232460962002804453118

a(9) <= 74322635218313783849790472504951802188239215127109371

If any a(k) of these values are less than presented values, one of a(k) + m is divisible only by at least one p^7 for some p > 31, 0 <= m < k.

For a(6) this minimum prime is some prime p > 59. (End)

References

J.-M. De Koninck, Those Fascinating Numbers, Entry 242, p. 63, Amer. Math. Soc., 2009.

Links

Table of n, a(n) for n=1..6.

David A. Corneth, PARI program for finding candidates

Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., (2009), page 63.

Example

2372890624 is divisible by 2^7, 2372890625 is divisible by 5^7, 2372890626 is divisible by 3^7.  This is the smallest number with this property, so a(3)=2372890624.

Crossrefs

Cf. A045882, A271443, A001015.

Sequence in context: A239404 A220301 A323541 * A016795 A222054 A338110

Adjacent sequences: A330483 A330484 A330485 * A330487 A330488 A330489

Keyword

nonn,more,hard

Author

Jud McCranie, Dec 15 2019

Extensions

a(5) from Giovanni Resta, Dec 17 2019

a(6) from Giovanni Resta, Dec 19 2019

Status

approved