cp's OEIS Frontend

Conjecture: the next terms are: 288230376151711745, 77371252455336267181195265, 20282409603651670423947251286017, 21267647932558653966460912964485513217.

Conjecture: prime terms are in A258429: 2, 5, 17, 65537.

Conjecture: corresponding primes p are Mersenne primes (A000668) > 3.

Sigma is multiplicative, and sigma(m) > 1 for all m > 1, so sigma(m) can be prime only if m is a prime power. Hence all n in this sequence are of the form 2^m + 1 for some m >= 0. This proves the above conjectures and leads to an explicit formula (q.v.) in terms of the Mersenne numbers. - Charles R Greathouse IV, Mar 01 2017

Conjecturally, a supersequence of A281312.

The conjecture is true: the formula at A281312 implies that the number of divisors of 4*A281312(n) - 4 is A000043(n+1). - Charles R Greathouse IV, Mar 01 2017

Corresponding pairs of numbers (tau(m-1)-1, k): (0, 0); (2, 2); (4, 2); (3, 3); (5, 5); (15, 3); (16, 4); (7, 7); ...

Numbers from A125137 (numbers of the form p^p + 1 where p = prime) are terms: 285311670612, 302875106592254, 827240261886336764178, 1978419655660313589123980, 20880467999847912034355032910568, ...

Prime terms are in A258429: 2, 5, 17, 65537, ...

A Fermat prime from A019434 of the form F(n) = 2^(2^n) + 1 is a term if k = 2^n * log(2) / log(2^n) is an integer.

a(11), if it exists, is > 10^10. - Lars Blomberg, Nov 14 2016