Saturday, April 21, 2018

Number of the day: 60509

Properties of the number 60509:

60509 is a cyclic number.
60509 is the 6101th prime.
60509 has 15 antidivisors and 60508 totatives.
60509 has an oblong digit sum 20 in base 10.
60509 = 302552 - 302542 is the difference of 2 nonnegative squares in 1 way.
60509 is the sum of 2 positive triangular numbers.
60509 is the difference of 2 positive pentagonal numbers in 1 way.
60509 = 222 + 2452 is the sum of 2 positive squares in 1 way.
60509 = 102 + 532 + 2402 is the sum of 3 positive squares.
605092 = 107802 + 595412 is the sum of 2 positive squares in 1 way.
605092 is the sum of 3 positive squares.
60509 is a proper divisor of 532161 - 1.
60509 is an emirp in (at least) the following bases: 4, 5, 6, 22, 26, 33, 38, 40, 44, 47, 58, 62, 67, 73, 77, 83, and 92.
60509 is palindromic in (at least) the following bases: 45, and 51.
60509 in base 45 = TdT and consists of only the digits 'T' and 'd'.
60509 in base 51 = NDN and consists of only the digits 'D' and 'N'.

The number 60509 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A018847: Strobogrammatic primes: the same upside down (calculator-style numerals).
A028883: Primes of form n^2 - 7.
A105378: Primes from merging of 5 successive digits in decimal expansion of Zeta(2) or (Pi^2)/6.
A201487: Primes of the form 5n^2 + 9.
A242385: Lesser of consecutive primes such that their average is of the form k*(k+2), for some integer k.
A242991: Smallest prime p such that p - floor(sqrt(p))^2 = n^2.

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