Friday, May 31, 2019

Number of the day: 950

Properties of the number 950:

950 = 2 × 52 × 19 is the 788th composite number and is not squarefree.
950 has 3 distinct prime factors, 12 divisors, 9 antidivisors and 360 totatives.
950 has a semiprime digit sum 14 in base 10.
950 is the difference of 2 positive pentagonal numbers in 2 ways.
950 = 32 + 102 + 292 is the sum of 3 positive squares.
9502 = 5702 + 7602 = 2662 + 9122 is the sum of 2 positive squares in 2 ways.
9502 is the sum of 3 positive squares.
950 is a proper divisor of 1512 - 1.
950 is palindromic in (at least) the following bases: 37, 49, 94, -15, and -73.
950 in base 6 = 4222 and consists of only the digits '2' and '4'.
950 in base 7 = 2525 and consists of only the digits '2' and '5'.
950 in base 8 = 1666 and consists of only the digits '1' and '6'.
950 in base 30 = 11k and consists of only the digits '1' and 'k'.

The number 950 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000601: Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)).
A001318: Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ....
A005449: Second pentagonal numbers: a(n) = n*(3*n + 1)/2.
A023894: Number of partitions of n into prime power parts (1 excluded).
A024702: a(n) = (prime(n)^2 - 1)/24.
A028338: Triangle of coefficients in expansion of (x+1)*(x+3)*...*(x + 2n - 1) in rising powers of x.
A028895: 5 times triangular numbers: a(n) = 5*n*(n+1)/2.
A035959: Number of partitions of n in which no parts are multiples of 5.
A084646: Hypotenuses for which there exist exactly 2 distinct integer triangles.
A304714: Number of connected strict integer partitions of n.

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