login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
1, 2, 9, 8, 36, 50, 241081, 117128, 15069924, 23011209, 95887457649, 92943436658, 31623999684484, 31716423048338, 48730521525625, 55647526914529, 202869088076944, 238595412613156, 316982950120225, 238595412613156, 12016309156631329, 9203885645879282 (list; graph; refs; listen; history; text; internal format)
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: A215025 A162954 A129194 * A272347 A214300 A092397

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 5 18:22 EDT 2021. Contains 346488 sequences. (Running on oeis4.)