Sunday, October 29, 2017

Number of the day: 1634

Properties of the number 1634:

1634 = 2 × 19 × 43 is a sphenic number and squarefree.
1634 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 756 totatives.
1634 has a semiprime digit sum 14 in base 10.
1634 has an oblong digit product 72 in base 10.
1634 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
1634 = 72 + 82 + 392 is the sum of 3 positive squares.
16342 is the sum of 3 positive squares.
1634 is a proper divisor of 12912 - 1.
1634 is palindromic in (at least) the following bases: 13, 24, 42, 85, -32, -34, and -71.
1634 in base 13 = 989 and consists of only the digits '8' and '9'.
1634 in base 16 = 662 and consists of only the digits '2' and '6'.
1634 in base 24 = 2k2 and consists of only the digits '2' and 'k'.
1634 in base 28 = 22a and consists of only the digits '2' and 'a'.

The number 1634 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002961: Numbers n such that n and n+1 have same sum of divisors.
A003321: Smallest n-th order perfect digital invariant or PDI: smallest number > 1 equal to sum of n-th powers of its digits, or 0 if no such number.
A005188: Armstrong (or Plus Perfect, or narcissistic) numbers: n-digit numbers equal to sum of n-th powers of their digits (a finite sequence, the last term being 115132219018763992565095597973971522401).
A014576: Smallest n-digit narcissistic (or Armstrong) number: smallest n-digit number equal to sum of n-th powers of its digits (or 0 if no such number exists).
A022267: a(n) = n*(9*n + 1)/2.
A023052: Powerful numbers (3): numbers n that are the sum of some fixed power of their digits.
A028557: n(n+5).
A056109: Fifth spoke of a hexagonal spiral.
A252648: Irregular table of perfect digital invariants for n > 1, i.e., numbers equal to the sum of n-th powers of their digits, read by rows.
A268261: T(n,k)=Number of length-(n+1) 0..k arrays with new repeated values introduced in sequential order starting with zero.

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