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