129,961

13² × 769

129,961 has digital root 1. The neighboring primes are 129959 and 129967; its proper-divisor sum differs from the starting integer by -119,012.

Prime Factor Structure

Factorization String 13^2 × 769

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 6

Divisor Sum (σ) 140,910

Proper Divisor Sum 10,949

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #129959 ← → #129967

Radix Representation

Decimal	129961
Binary	11111101110101001 (17 bits)
Octal	0o375651
Hexadecimal	0x1FBA9

Divisor Catalog (6)

1 13 169 769 9,997 129,961

Collatz Trajectory (131 steps to reach 1)

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

129,961 389,884 194,942 97,471 292,414 146,207 438,622 219,311 657,934 328,967 986,902 493,451 1,480,354 740,177 2,220,532 1,110,266 555,133 1,665,400 832,700 416,350 208,175 624,526 312,263 936,790 468,395 1,405,186 702,593 2,107,780 1,053,890 526,945 1,580,836 790,418 395,209 1,185,628 592,814 296,407 889,222 444,611 1,333,834 666,917 2,000,752 1,000,376 500,188 250,094 125,047 375,142 187,571 562,714 281,357 844,072 422,036 211,018 105,509 316,528 158,264 79,132 39,566 19,783 59,350 29,675

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