Oblong number
A oblong number , or number pronic or number heteromecic , is a number which is the product of two whole natural consecutive, i.e., N ( N + 1). Each oblong number for N is also the double of the triangular Nombre for N . The first oblong small numbers are:
0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056,1122,1190,1260,1332,1406,1482,1560,1640,1722,1806,1892,1980,2070,2162
The oblong numbers can also be expressed in the form . The oblong number for N is also the sum of the whole first even N , or like the difference between and N ième hexagonal Nombre centered.
In a clear way, 2 is only the Prime number oblong. It is also the only oblong number in the Suite of Fibonacci.
The value of the Function of Möbius, μ ( X ) for any oblong number, in addition to being calculable in a usual way, can also be calculated by multiplying μ ( N ) by μ ( N + 1). If N or the following neighbor is Without square, then, obviously, the result will not be an oblong number. Perhaps not in a so obvious way, if N and its neighbor (both) is numbers with an even number of factors first, the resulting oblong number will have also an even number of factors first. These observations rise from the multiplicative properties which the function of Möbius has and owing to the fact that the consecutive entireties are Premiers between them.
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