

A279095


Smallest k such that sigma(2^(k*n)) is prime.


0



1, 1, 2, 1, 6, 1, 18, 2, 2, 3, 8, 1, 40, 9, 2, 1, 177728, 1, 120, 3, 6, 4, 32906, 95, 868, 20, 1648, 346
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OFFSET

1,3


COMMENTS

Equivalently, smallest k such that k*n + 1 is a Mersenne exponent (A000043).
As of Mar 11 2017, the jth Mersenne exponent A000043(j) is known for j=1..45; four additional terms of A000043 are listed in the Extensions for that sequence, but it is not yet known whether they are A000043(46) through A000043(49). None of the first 45 Mersenne exponents are of the form k*29 + 1, so a(29) > floor((A000043(45)  1)/29) = floor((37156667  1)/29) = 1281264. However, one of the four additional terms is 57885161 = 1996040*29 + 1; thus, 1281264 < a(29) <= 1996040.
a(30) through a(38) are 1, 700, 623, 134, 88864, 284, 1236, 821688, 60.
a(39) > floor((A000043(45)  1)/39) = 952735.
This sequence coincides with A186283 (Least number k such that k*n+1 is a prime dividing 2^n1) from a(2) through a(8), but a(9) = 2 whereas A186283(9) = 8.


LINKS

Table of n, a(n) for n=1..28.


EXAMPLE

a(1) = 1 because sigma(2^(1*1)) = sigma(2) = 1 + 2 = 3 is prime. (1*1 + 1 = 2 = A000043(1).)
a(3) = 2 because sigma(2^(1*3)) = sigma(2^3) = 1 + 2 + 4 + 8 = 15 is not prime, but sigma(2^(2*3)) = sigma(2^6) = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 is prime. (1*3 + 1 = 4 is not in A000043, but 2*3 + 1 = 7 = A000043(4).)
a(17) = 177728 because sigma(2^(177728*17)) is prime and sigma(2^(k*17)) is not prime for any k < 177728. (177728*17 + 1 = 3021377 = A000043(37), and no Mersenne exponent less than A000043(37) is of the form k*17 + 1.)


PROG

(PARI) a(n) = k=1; while(!isprime(sigma(2^(k*n))), k++); k; \\ Michel Marcus, Mar 12 2017


CROSSREFS

Cf. A000043, A000203, A186283, A279004.
Sequence in context: A322672 A225769 A280736 * A186283 A307374 A173279
Adjacent sequences: A279092 A279093 A279094 * A279096 A279097 A279098


KEYWORD

nonn,hard,more


AUTHOR

Jon E. Schoenfield, Mar 11 2017


STATUS

approved



