35 @ Sofia, Република България!

Pyramid_of_35_spheres_animation

35 is the sum of the first five triangular numbers, making it a tetrahedral number.

35 is a centered cube number, a pentagonal number and a pentatope number.

35 is a highly cototient number, since there are more solutions to the equation                 x – φ(x) = 35 than there are for any other integers below it except 1.

There are 35 hexominoes, the polyominoes made from 6 squares.

35 is a discrete semiprime (or biprime) (5 x 7); the tenth, and the first with 5 as the lowest non-unitary factor. The aliquot sum of 35 is 13 this being the second composite number with such an aliquot sum; the first being the cube 27. 35 is the last member of the first triple cluster of semiprimes 33,34,35. 85,86,87 is the second such triple discrete semiprime cluster.

Since the greatest prime factor of 352 + 1 = 1226 is 613, which is obviously more than 35 twice, 35 is a Størmer number.

35 is the highest number one can count to on one’s fingers using base 6.

and today, 35 years old!

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