

A069354


Lowest base with simple divisibility test for n primes; smallest B such that omega(B) + omega(B1) = n.


2



2, 3, 6, 15, 66, 210, 715, 7315, 38571, 254541, 728365, 11243155, 58524466, 812646121, 5163068911, 58720148851, 555409903686, 4339149420606
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OFFSET

1,1


COMMENTS

Indices of record values of primepi(n)  A181834(n) (the number of primes <= n which are not strongly prime to n).  Peter Luschny, Mar 17 2013
As pointed out by Don Reble on the SeqFan list, one has a(n) = A059958(n)+1 at least up to a(18), since so far A001221(m*(m+1)) = n (and not ">") for m = A059958(n).  M. F. Hasler, Jan 15 2014
10^13 < a(19) <= 69322940121436.  Giovanni Resta, Mar 24 2020


LINKS

Table of n, a(n) for n=1..18.
Peter Luschny, Strong coprimality, November 2010.
Robert Munafo, Low bases with many divisibility tests


FORMULA

a(n) = A059958(n) + 1 for 0 < n < 19.  Robert G. Wilson v, Feb 18 2014


EXAMPLE

a(4) = 15 because in base 15 you can test for divisibility by 4 different primes (3 and 5 directly, 2 and 7 by "casting out 14's")


MAPLE

A069354_list := proc(n) local i, L, Max; Max := 1; L := NULL;
for i from 2 to n do
if nops(numtheory[factorset](i*(i1))) = Max
then Max := Max + 1; L := L, i fi;
od;
L end: # Peter Luschny, Nov 12 2010


CROSSREFS

Cf. A001221, A181834.
Sequence in context: A060796 A059842 A001529 * A116632 A214343 A007364
Adjacent sequences: A069351 A069352 A069353 * A069355 A069356 A069357


KEYWORD

nonn,more


AUTHOR

Robert Munafo, Nov 19 2002


EXTENSIONS

More terms added using data from A059958 (see there for credits) by M. F. Hasler, Jan 15 2014


STATUS

approved



