λ
Harmonic Matrix

78,781

78781
Deficient Odd Prime

78,781 has digital root 4. The neighboring primes are 78779 and 78787; its proper-divisor sum differs from the starting integer by -78,780.

Prime Factor Structure

Factorization String 78781
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 78,782
Proper Divisor Sum 1
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #78779 ← → #78787

Radix Representation

Decimal 78781
Binary 10011001110111101 (17 bits)
Octal 0o231675
Hexadecimal 0x133BD

Divisor Catalog (2)

1 78,781

Collatz Trajectory (107 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

78,781 236,344 118,172 59,086 29,543 88,630 44,315 132,946 66,473 199,420 99,710 49,855 149,566 74,783 224,350 112,175 336,526 168,263 504,790 252,395 757,186 378,593 1,135,780 567,890 283,945 851,836 425,918 212,959 638,878 319,439 958,318 479,159 1,437,478 718,739 2,156,218 1,078,109 3,234,328 1,617,164 808,582 404,291 1,212,874 606,437 1,819,312 909,656 454,828 227,414 113,707 341,122 170,561 511,684 255,842 127,921 383,764 191,882 95,941 287,824 143,912 71,956 35,978 17,989

More profiles

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