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A276045 Primes p such that d(p*(2p+1))=8 where d(n) is the number of divisors of n (A000005). 2
7, 13, 17, 19, 43, 47, 59, 61, 71, 79, 101, 107, 109, 149, 151, 163, 167, 197, 223, 257, 263, 271, 311, 317, 347, 349, 353, 383, 389, 401, 421, 439, 449, 461, 479, 503, 521, 523, 557, 569, 599, 601, 613, 631, 673, 677, 691, 701, 811, 821, 827, 839, 853, 863, 881, 919 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that 2p+1 is in A030513. - Robert Israel, Aug 17 2016

Is this the union of {13} and A234095? - R. J. Mathar, Aug 28 2016

From Anthony Hernandez, Aug 29 2016: (Start)

Conjecture: this sequence is infinite.

It appears that the prime numbers in this sequence which have 7 for as final digit form the sequence A104164.

Conjecture: this sequence contains infinitely many twin primes. The first few twin primes in this sequence are 17,19,59,61,107,109,521,523,599,601,... (End)

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

d(7*(2*7+1))=d(105)=8 so 7 is a term.

MAPLE

select(n -> isprime(n) and numtheory:-tau(n*(2*n+1))=8,

[seq(i, i=3..1000, 2)]); # Robert Israel, Aug 17 2016

MATHEMATICA

Select[Prime@ Range@ 160, DivisorSigma[0, # (2 # + 1)] == 8 &] (* Michael De Vlieger, Aug 28 2016 *)

PROG

(PARI) lista(nn) = forprime(p=2, nn, if (numdiv(p*(2*p+1))==8, print1(p, ", "))); \\ Michel Marcus, Aug 17 2016

CROSSREFS

Cf. A000005, A030513, A030626.

Sequence in context: A147603 A106084 A110053 * A230039 A226138 A180263

Adjacent sequences:  A276042 A276043 A276044 * A276046 A276047 A276048

KEYWORD

nonn,easy

AUTHOR

Anthony Hernandez, Aug 17 2016

EXTENSIONS

More terms from Michel Marcus, Aug 17 2016

STATUS

approved

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Last modified June 17 16:29 EDT 2019. Contains 324195 sequences. (Running on oeis4.)