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
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
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