A300779 Odd numbers x such that x and x + 2 are both sums of divisors, i.e., elements of A000203.

1, 13, 91, 241573, 38152387, 139415801707, 55342019130181, 61166380109329, 417542026135897, 417542026135897, 13805828672331787

Offset

1,2

Comments

If some x or x + 2 is in A300869, i.e., it has more than one representation as sigma(m), as for x = 417542026135897 = sigma((4*17*209459)^2) = sigma((5*17*209459)^2) = sigma((2*7723267)^2) - 2, then it is listed with multiplicity and all corresponding pairs of numbers are provided in A300780.

Links

Table of n, a(n) for n=1..11.

Seqfan Mailing List Thread, Consecutive sigmas, with contributions from Franklin T. Adams-Watters, Hugo Pfoertner and Emmanuel Vantieghem.

Example

a(1) = 1 because 1 = sigma(1) and 3 = sigma(2),
a(2) = 13: 13 = sigma(9) and 15 = sigma(8),
a(3) = 91: 91 =sigma(36), 93 = sigma(50),
a(4) = 241573: 241573 = sigma(241081), 241575 = sigma(117128),
a(5) = 38152387: 38152387 = sigma(15069924), 38152389 = sigma(23011209).

Crossrefs

Cf. A000203, A002191, A083531, A300780 (numbers corresponding to sigma values), A300869.

Sequence in context: A022578 A090020 A092469 * A275918 A027670 A055608

Adjacent sequences: A300776 A300777 A300778 * A300780 A300781 A300782

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Mar 12 2018

Extensions

a(5) from Emmanuel Vantieghem

a(6)-a(11) from Giovanni Resta, Mar 13 2018

Status

approved