A276629 Primes p such that sigma(sigma(p-1)) is a power of 2.

2, 3, 5, 17, 101, 1601, 65537, 2365849601

Offset

1,1

Comments

Primes p such that A051027(p-1) = A000203(A000203(p-1)) is a power of 2.

Corresponding values of powers: 1, 4, 8, 32, 256, 4096, 131072, 8589934592, ...

Corresponding values of exponents: 0, 2, 3, 5, 8, 12, 17, 33, ...

If a(9) exists, it must be greater than 2*10^11.

Links

Table of n, a(n) for n=1..8.

Example

Prime 5 is in this sequence because A051027(5) = 8 = 2^3.

Mathematica

Select[Prime@ Range[10^5], IntegerQ@ Log2@ Nest[DivisorSigma[1, #] &, # - 1, 2] &] (* Michael De Vlieger, Sep 08 2016 *)

Prog

(Magma) [2] cat [n: n in[3..10^8] | IsPrime(n) and IsPower(SumOfDivisors(SumOfDivisors(n-1))) and &+[d: d in PrimeDivisors(SumOfDivisors(SumOfDivisors(n-1)))] eq 2]
(PARI) lista(nn) = forprime(p=2, nn, if (ispower(sigma(sigma(p-1)), , &k) && (k==2), print1(p, ", "))); \\ Michel Marcus, Sep 08 2016

Crossrefs

Cf. A000203, A051027, A275674.

Sequence in context: A089983 A370606 A072858 * A218086 A291049 A087911

Adjacent sequences: A276626 A276627 A276628 * A276630 A276631 A276632

Keyword

nonn,more

Author

Jaroslav Krizek, Sep 07 2016

Extensions

a(8) from Lars Blomberg, Jan 04 2017

Status

approved