A084116 Numbers m such that A084115(m) = 1.

2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 119

Offset: 1

Author

Reinhard Zumkeller, May 12 2003

Keywords

• nonn

Comments

A084113(a(n)) = A084114(a(n)) + 1.

Union of primes and multiplicatively perfect numbers (A000040, A007422).

A084115(a(n)) = 1; A066729(a(n)) = a(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Multiplicative Perfect Number.

Crossrefs

Cf. A084110, A066729, A084113, A084114, A084115, A066423 (complement).

Programs

Haskell

a084116 n = a084116_list !! (n-1)
a084116_list = filter ((== 1) . a084115) [1..]
-- Reinhard Zumkeller, Jul 31 2014

Mathematica

Select[Range[2, 200], PrimeQ[DivisorSigma[0, #]^DivisorSigma[0, #] + 1] &] (* Carl Najafi, Oct 19 2011 *)

PARI

is(n)=isprime(n) || numdiv(n) == 4 \\ Charles R Greathouse IV, Oct 19 2015

Formula

It appears that a(n) = n such that A000005(n)^A000005(n)+1 is prime. - Carl Najafi, Oct 19 2011

Extensions

Corrected and edited by Carl Najafi, Oct 19 2011

Revised by Reinhard Zumkeller, Jul 31 2014