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Atlas › Integer Profiles › Node 40,129,904

40,129,904

24 × 37 × 53 × 1279
Abundant Even Composite

40,129,904 factors as 2^4 × 37 × 53 × 1279. Its 40 positive divisors give a proper-divisor sum of 41,293,456, so this integer is abundant. The Collatz stopping time is 284 steps.

Prime Factor Structure

Factorization String 2^4 × 37 × 53 × 1279
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 81,423,360
Proper Divisor Sum 41,293,456
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #40129897 ← → #40129907

Radix Representation

Decimal 40129904
Binary 10011001000101010101110000 (26 bits)
Octal 0o231052560
Hexadecimal 0x2645570

Divisor Catalog (40)

1 2 4 8 16 37 53 74 106 148 212 296 424 592 848 1,279 1,961 2,558 3,922 5,116 7,844 10,232 15,688 20,464 31,376 47,323 67,787 94,646 135,574 189,292 271,148 378,584 542,296 757,168 1,084,592 2,508,119 5,016,238 10,032,476 20,064,952 40,129,904

Collatz Trajectory (284 steps to reach 1)

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

40,129,904 20,064,952 10,032,476 5,016,238 2,508,119 7,524,358 3,762,179 11,286,538 5,643,269 16,929,808 8,464,904 4,232,452 2,116,226 1,058,113 3,174,340 1,587,170 793,585 2,380,756 1,190,378 595,189 1,785,568 892,784 446,392 223,196 111,598 55,799 167,398 83,699 251,098 125,549 376,648 188,324 94,162 47,081 141,244 70,622 35,311 105,934 52,967 158,902 79,451 238,354 119,177 357,532 178,766 89,383 268,150 134,075 402,226 201,113 603,340 301,670 150,835 452,506 226,253 678,760 339,380 169,690 84,845 254,536

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