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A291194 Numbers k having at least one prime factor p such that p^2 divides 2^(k-1) - 1. 0
1093, 3511, 398945, 796797, 1194649, 1592501, 1990353, 2388205, 2786057, 3183909, 3581761, 3979613, 4377465, 4775317, 5173169, 5571021, 5968873, 6165316, 6366725, 6764577, 7162429, 7560281, 7958133, 8355985, 8753837, 9151689, 9549541, 9947393, 10345245 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Another version of A001220.

Sequence is infinite since if k is a term then also k^m is a term, for every m >= 2.

What is the smallest number in this sequence which is not of the form 13*n + 1?

Complete factorizations of the first 15 terms:

a(1)  = 1093

a(2)  = 3511

a(3)  = 5 * 73 * 1093

a(4)  = 3^6 * 1093

a(5)  = 1093^2

a(6)  = 31 * 47 * 1093

a(7)  = 3 * 607 * 1093

a(8)  = 5 * 19 * 23 * 1093

a(9)  = 1093 * 2549

a(10) = 3 * 971 * 1093

a(11) = 29 * 113 * 1093

a(12) = 11 * 331 * 1093

a(13) = 3^2 * 5 * 89 * 1093

a(14) = 17 * 257 * 1093

a(15) = 1093 * 4733

LINKS

Table of n, a(n) for n=1..29.

PROG

(MAGMA) lst:=[]; for n in [2..10345245] do f:=Factorization(n); if not IsNull([x: x in [1..#f] | Modexp(2, n-1, f[x][1]^2) eq 1]) then Append(~lst, n); end if; end for; lst;

CROSSREFS

Cf. A190991, A270833. A001220 gives the primes.

Sequence in context: A291961 A001220 A265630 * A270833 A273471 A266829

Adjacent sequences:  A291191 A291192 A291193 * A291195 A291196 A291197

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Aug 20 2017

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)