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Perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4]
An extravagant number has fewer digits than its prime factorization. The first in decimal: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30 (sequence A046760 in the OEIS ). An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital.
Primes for which there are more prime permutations of some or all the decimal digits than for any smaller number. 2 , 13 , 37 , 107 , 113 , 137 , 1013 , 1237 , 1367 , 10079 ( OEIS : A119535 )
Smallest base which is not perfect odd power (where generalized Wagstaff numbers can be factored algebraically) for which no generalized Wagstaff primes are known. 100: Centesimal: As 100=10 2, these are two decimal digits. 121: Number expressible with two undecimal digits. 125: Number expressible with three quinary digits. 128: Using as 128=2 7.
Ribenboim defines a triply palindromic prime as a prime p for which: p is a palindromic prime with q digits, where q is a palindromic prime with r digits, where r is also a palindromic prime. [5] For example, p = 10 11310 + 4661664 × 10 5652 + 1, which has q = 11311 digits, and 11311 has r = 5 digits. The first (base-10) triply palindromic ...
n with an odd number of distinct prime factors (μ(n)=-1) 4 6 32 64 351 617 3438 6067 + + n even with an odd number of prime factors 1 2 9 21 100 180 1010 6067 + + n even with an odd number of distinct prime factors 3 4 21 49 268 482 2486 4452 + + n odd with an odd number of prime factors 3 4 23 43 251 437 2428 4315 + +
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The smallest odd abundant number is 945. The smallest abundant number not divisible by 2 or by 3 is 5391411025 whose distinct prime factors are 5, 7, 11, 13, ...