A300780 - OEIS

%I #22 Jun 25 2018 02:56:59

%S 1,2,9,8,36,50,241081,117128,15069924,23011209,95887457649,

%T 92943436658,31623999684484,31716423048338,48730521525625,

%U 55647526914529,202869088076944,238595412613156,316982950120225,238595412613156,12016309156631329,9203885645879282

%N 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.

%C So far, a(2n-1) is always a square. Will this always hold? - _M. F. Hasler_, Mar 12 2018

%e a(1) = 1, a(2) = 2 because sigma(2) - sigma(1) = 3 - 1 = 2.

%e a(3) = 9, a(4) = 8 because sigma(8) - sigma(9) = 15 - 13 = 2.

%e a(5) = 36, a(6) = 50 because sigma(50) - sigma(36) = 93 - 91 = 2.

%e 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

%Y Cf. A000203, A002191, A300779.

%K nonn,hard

%O 1,2

%A _Hugo Pfoertner_, Mar 12 2018

%E a(11)-a(22) from _Giovanni Resta_, Mar 13 2018