Tuesday, March 5, 2019

Number of the day: 3010

Properties of the number 3010:

3010 = 2 × 5 × 7 × 43 is the 2578th composite number and is squarefree.
3010 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1008 totatives.
3010 has a semiprime digit sum 4 in base 10.
3010 is the sum of 2 positive triangular numbers.
3010 is the difference of 2 positive pentagonal numbers in 5 ways.
3010 = 32 + 202 + 512 is the sum of 3 positive squares.
30102 = 18062 + 24082 is the sum of 2 positive squares in 1 way.
30102 is the sum of 3 positive squares.
3010 is a proper divisor of 6012 - 1.
3010 is palindromic in (at least) the following bases: 9, 19, 31, 32, 51, 69, 85, -21, -47, and -59.
3010 in base 3 = 11010111 and consists of only the digits '0' and '1'.
3010 in base 9 = 4114 and consists of only the digits '1' and '4'.
3010 in base 19 = 868 and consists of only the digits '6' and '8'.
3010 in base 20 = 7aa and consists of only the digits '7' and 'a'.
3010 in base 24 = 55a and consists of only the digits '5' and 'a'.
3010 in base 30 = 3aa and consists of only the digits '3' and 'a'.
3010 in base 31 = 343 and consists of only the digits '3' and '4'.
3010 in base 32 = 2u2 and consists of only the digits '2' and 'u'.
3010 in base 50 = 1AA and consists of only the digits '1' and 'A'.
3010 in base 51 = 181 and consists of only the digits '1' and '8'.

The number 3010 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000041: a(n) is the number of partitions of n (the partition numbers).
A000566: Heptagonal numbers (or 7-gonal numbers): n(5n-3)/2.
A035363: Number of partitions of n into even parts.
A035928: Numbers n such that BCR(n) = n, where BCR = binary-complement-and-reverse = take one's complement then reverse bit order.
A052001: Even partition numbers.
A052218: Numbers whose sum of digits is 4.
A059845: a(n) = n*(3*n + 11)/2.
A100039: Positions of occurrences of the natural numbers as fourth subsequence in A100035.
A121030: Multiples of 10 containing a 10 in their decimal representation.
A139063: Numbers k for which (6+k!)/6 is prime.

No comments:

Post a Comment