A300780 Pairs of numbers producing consecutive odd sums of divisors, i.e., sigma(a(2*k)) = sigma(a(2*k-1)) + 2, with sigma values given in A300779.

1, 2, 9, 8, 36, 50, 241081, 117128, 15069924, 23011209, 95887457649, 92943436658, 31623999684484, 31716423048338, 48730521525625, 55647526914529, 202869088076944, 238595412613156, 316982950120225, 238595412613156, 12016309156631329, 9203885645879282

Offset

1,2

Comments

So far, a(2n-1) is always a square. Will this always hold? - M. F. Hasler, Mar 12 2018

Links

Table of n, a(n) for n=1..22.

Example

a(1) = 1, a(2) = 2 because sigma(2) - sigma(1) = 3 - 1 = 2.
a(3) = 9, a(4) = 8 because sigma(8) - sigma(9) = 15 - 13 = 2.
a(5) = 36, a(6) = 50 because sigma(50) - sigma(36) = 93 - 91 = 2.
The first pairs have the following factorization: (3^2, 2*2^2), (6^2, 2*5^2), (491^2, 2*(2*11^2)^2), ((2*3*647)^2, (3^2*13*41)^2). - M. F. Hasler, Mar 12 2018

Crossrefs

Cf. A000203, A002191, A300779.

Sequence in context: A162954 A357993 A129194 * A272347 A371255 A214300

Adjacent sequences: A300777 A300778 A300779 * A300781 A300782 A300783

Keyword

nonn,hard

Author

Hugo Pfoertner, Mar 12 2018

Extensions

a(11)-a(22) from Giovanni Resta, Mar 13 2018

Status

approved