A330486 - OEIS

%I #23 Dec 19 2019 12:33:36

%S 128,76544,2372890624,390491792890623,2083234733888734218749,

%T 18962123650219836035505781245

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

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

%C From _David A. Corneth_, Dec 18 2019: (Start)

%C a(6) <= 18962123650219836035505781245

%C a(7) <= 105574810222799317012520534891328125

%C a(8) <= 352061173826332779662070232460962002804453118

%C a(9) <= 74322635218313783849790472504951802188239215127109371

%C 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.

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

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

%H David A. Corneth, <a href="/A330486/a330486.gp.txt">PARI program for finding candidates</a>

%H Jean-Marie De Koninck, <a href="https://bookstore.ams.org/mbk-64/83">Those Fascinating Numbers</a>, Amer. Math. Soc., (2009), page 63.

%e 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.

%Y Cf. A045882, A271443, A001015.

%K nonn,more,hard

%O 1,1

%A _Jud McCranie_, Dec 15 2019

%E a(5) from _Giovanni Resta_, Dec 17 2019

%E a(6) from _Giovanni Resta_, Dec 19 2019