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A273202
Minimal terms of A274720.
2
9, 21, 25, 39, 49, 55, 57, 111, 121, 155, 169, 183, 201, 203, 205, 219, 237, 253, 289, 291, 301, 305, 309, 327, 355, 361, 417, 453, 489, 497, 505, 529, 543, 579, 597, 633, 655, 689, 723, 737, 755, 791, 813, 841, 889, 905, 921, 939, 955, 961, 979, 993, 1011
OFFSET
1,1
COMMENTS
Terms m of A274720 such that no nontrivial divisor of m is in A274720.
The terms consist of the following:
p^(b+1) where p is an odd prime and b is the largest exponent k such that p^k divides 2^(p-1)-1 (in particular b=1 if p is not a Wieferich prime).
p*q where p < q are odd primes and p divides the order of 2 mod q.
LINKS
EXAMPLE
39 is a term because it is in A274720 and its nontrivial divisors 3 and 13 are not in A274720.
MAPLE
N:= 10000: # less than 1093^2 so we don't need to worry about powers of
# Wieferich primes
Primes:= select(isprime, [seq(i, i=3..N/3)]):
S:= {}:
for q in Primes do
m:= numtheory:-order(2, q);
ps:= numtheory:-factorset(m) union {q} minus {2};
S:= S union select(`<=`, map(`*`, ps, q), N)
od:
sort(convert(S, list));
MATHEMATICA
A274720 = Select[Range[1, 2000, 2], !CoprimeQ[MultiplicativeOrder[2, #], #]&]; Select[A274720, NoneTrue[Divisors[#][[2;; -2]], MemberQ[A274720, #]&]&] (* Jean-François Alcover, Apr 27 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Jul 27 2016
STATUS
approved