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A165319
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Primes p where the number of divisors of p+1 is a power of 2.
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3
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2, 5, 7, 13, 23, 29, 37, 41, 53, 61, 73, 101, 103, 109, 113, 127, 137, 151, 157, 167, 173, 181, 193, 229, 257, 263, 269, 277, 281, 311, 313, 317, 353, 373, 383, 389, 397, 401, 409, 421, 433, 439, 457, 461, 487, 509, 541, 569, 593, 601, 613, 617, 631, 641, 653
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OFFSET
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1,1
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..20000
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MAPLE
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b:= proc(n) option remember; is(n=2^ilog2(n)) end:
a:= proc(n) option remember; local p; p:= `if`(n=1, 1, a(n-1));
do p:= nextprime(p);
if andmap(b, map(i-> i[2]+1, ifactors(p+1)[2])) then break fi
od; p
end:
seq(a(n), n=1..55); # Alois P. Heinz, Sep 05 2019
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MATHEMATICA
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okQ[p_] := PrimeQ[p] && IntegerQ[Log[2, DivisorSigma[0, p+1]]];
Select[Prime[Range[200]], okQ] (* Jean-François Alcover, May 20 2020 *)
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PROG
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(PARI) isok(p) = isprime(p) && (nd = numdiv(p+1)) && (nd == 2^valuation(nd, 2)); \\ Michel Marcus, Sep 05 2019
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CROSSREFS
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Cf. A165318, A165320.
Cf. A008329. [R. J. Mathar, Sep 20 2009]
Sequence in context: A261581 A045355 A252281 * A094712 A095281 A106889
Adjacent sequences: A165316 A165317 A165318 * A165320 A165321 A165322
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet, Sep 14 2009
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EXTENSIONS
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Extended by R. J. Mathar, Sep 20 2009
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STATUS
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approved
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