Tuesday, August 1, 2017

Number of the day: 73457

Properties of the number 73457:

73457 is a cyclic number.
73457 = 17 × 29 × 149 is a sphenic number and squarefree.
73457 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 66304 totatives.
73457 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 73457 results in a prime.
73457 = (48 × 49)/2 + … + (81 × 82)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
73457 = 367292 - 367282 = 21692 - 21522 = 12812 - 12522 = 3212 - 1722 is the difference of 2 nonnegative squares in 4 ways.
73457 is the difference of 2 positive pentagonal numbers in 4 ways.
73457 = 892 + 2562 = 42 + 2712 = 1842 + 1992 = 1242 + 2412 is the sum of 2 positive squares in 4 ways.
73457 = 142 + 192 + 2702 is the sum of 3 positive squares.
734572 = 345682 + 648152 = 102952 + 727322 = 490682 + 546652 = 230952 + 697322 = 21682 + 734252 = 455682 + 576152 = 196682 + 707752 = 57452 + 732322 = 427052 + 597682 = 506602 + 531932 = 293932 + 673202 = 326402 + 658072 = 251432 + 690202 is the sum of 2 positive squares in 13 ways.
734572 is the sum of 3 positive squares.
73457 is a proper divisor of 70128 - 1.
73457 = '7' + '3457' is the concatenation of 2 prime numbers.
73457 = '734' + '57' is the concatenation of 2 semiprime numbers.
73457 is palindromic in (at least) the following bases: 2, and 42.
73457 in base 42 = fQf and consists of only the digits 'Q' and 'f'.
73457 in base 56 = NNf and consists of only the digits 'N' and 'f'.

The number 73457 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A090508: Least number beginning with prime(n) such that every concatenation is a prime.
A253131: Number of length 3+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero

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