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A215150
Pseudoprimes divisible by a smaller pseudoprime.
2
13981, 18705, 23001, 55245, 63973, 72885, 75361, 107185, 126217, 129921, 137149, 157641, 158369, 172081, 176149, 188461, 215265, 266305, 272251, 276013, 278545, 285541, 294409, 348161, 387731, 423793, 464185, 488881, 493697, 617093, 625921, 743665, 748657, 825265
OFFSET
1,1
COMMENTS
Here pseudoprime means a Fermat base-2 pseudoprime (a member of A001567).
Pseudoprimes by which the numbers from sequence are divisible: 341, 645, 561, 1905, 1729, 645, 341, 1105, 1387 and 1729, 341, 2047, 561, 5461, 2821, 1387, 1729, 1905, 1105, 2047, 1387, 2465 and 3277, 4681, 2701 and 4033 and 7957, 341, 5461, 4369, 5461, 2701, 4369, 5461, 10261, 1105, 1729, 1387 and 11305.
A pseudoprime can be divisible by more than one pseudoprime: e.g. 126217, 278545, 294409, 825265.
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 13981
Eric Weisstein's World of Mathematics, Poulet Number
EXAMPLE
Since 2^13980 = 1 mod 13981 and 13981 = 11 * 31 * 41, 13981 is a pseudoprime, and it is divisible by 341, a smaller pseudoprime. 13981 is therefore in the sequence.
The pseudoprimes 75361, 129921, 348161, etc., are also divisible by 341.
MATHEMATICA
lst1 = {}; lst2 = {}; r = 10^6; Do[If[! PrimeQ[n] && PowerMod[2, n - 1, n] == 1, AppendTo[lst1, n]], {n, 1, r, 2}]; l = Length[lst1]; Do[p = lst1[[a]]; b = 1; While[True, t = lst1[[b]]; If[p < 3*t, Break[]]; If[Divisible[p, t], AppendTo[lst2, p]; Break[]]; b++], {a, 2, l}]; lst2
CROSSREFS
Sequence in context: A031666 A031819 A066939 * A215944 A248999 A251612
KEYWORD
nonn
AUTHOR
STATUS
approved