λ
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Atlas › Integer Profiles › Node 96,876,192

96,876,192

25 × 3 × 7 × 144161
Abundant Even Composite

96,876,192 factors as 2^5 × 3 × 7 × 144161. Its 48 positive divisors give a proper-divisor sum of 193,754,400, so this integer is abundant. The Collatz stopping time is 187 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 7 × 144161
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 290,630,592
Proper Divisor Sum 193,754,400
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #96876191 ← → #96876223

Radix Representation

Decimal 96876192
Binary 101110001100011011010100000 (27 bits)
Octal 0o561433240
Hexadecimal 0x5C636A0

Divisor Catalog (48)

1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 56 84 96 112 168 224 336 672 144,161 288,322 432,483 576,644 864,966 1,009,127 1,153,288 1,729,932 2,018,254 2,306,576 3,027,381 3,459,864 4,036,508 4,613,152 6,054,762 6,919,728 8,073,016 12,109,524 13,839,456 16,146,032 24,219,048 32,292,064 48,438,096 96,876,192

Collatz Trajectory (187 steps to reach 1)

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

96,876,192 48,438,096 24,219,048 12,109,524 6,054,762 3,027,381 9,082,144 4,541,072 2,270,536 1,135,268 567,634 283,817 851,452 425,726 212,863 638,590 319,295 957,886 478,943 1,436,830 718,415 2,155,246 1,077,623 3,232,870 1,616,435 4,849,306 2,424,653 7,273,960 3,636,980 1,818,490 909,245 2,727,736 1,363,868 681,934 340,967 1,022,902 511,451 1,534,354 767,177 2,301,532 1,150,766 575,383 1,726,150 863,075 2,589,226 1,294,613 3,883,840 1,941,920 970,960 485,480 242,740 121,370 60,685 182,056 91,028 45,514 22,757 68,272 34,136 17,068

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