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The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...
A doorjamb, door jamb, or sometimes doorpost is the vertical portion of the door frame onto which a door is secured. [3] The jamb bears the weight of the door through its hinges, and most types of door latches and deadbolts extend into a recess in the doorjamb when engaged, making the accuracy of the plumb (i.e. true vertical) and strength of ...
0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add" : a (0) = 0; for n > 0, a ( n ) = a ( n − 1) − n if that number is positive and not already in the sequence, otherwise a ( n ) = a ( n − 1) + n , whether or not that number is already in the sequence.
The purpose of this page is to catalog new, interesting, and useful identities related to number-theoretic divisor sums, i.e., sums of an arithmetic function over the divisors of a natural number , or equivalently the Dirichlet convolution of an arithmetic function () with one:
That is, the digital sum is the same as the normal sum except that no carrying is used. For example, in decimal (base 10) arithmetic, the digital sum of 123 and 789 is 802: 3 + 9 = 12, discard the 10 leaving 2. 2 + 8 = 10, discard the 10 leaving 0. 1 + 7 = 8, there is no carry to discard. 123 789 --- 802
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Then the triangle is in Euclidean space if the sum of the reciprocals of p, q, and r equals 1, spherical space if that sum is greater than 1, and hyperbolic space if the sum is less than 1. A harmonic divisor number is a positive integer whose divisors have a harmonic mean that is an integer. The first five of these are 1, 6, 28, 140, and 270.