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Atlas › Integer Profiles › Node 37,742,005

37,742,005

5 × 73 × 59 × 373
Deficient Odd Composite

37,742,005 factors as 5 × 7^3 × 59 × 373. Its 32 positive divisors give a proper-divisor sum of 16,113,995, so this integer is deficient. The Collatz stopping time is 178 steps.

Prime Factor Structure

Factorization String 5 × 7^3 × 59 × 373
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 53,856,000
Proper Divisor Sum 16,113,995
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #37741943 ← → #37742041

Radix Representation

Decimal 37742005
Binary 10001111111110010110110101 (26 bits)
Octal 0o217762665
Hexadecimal 0x23FE5B5

Divisor Catalog (32)

1 5 7 35 49 59 245 295 343 373 413 1,715 1,865 2,065 2,611 2,891 13,055 14,455 18,277 20,237 22,007 91,385 101,185 110,035 127,939 154,049 639,695 770,245 1,078,343 5,391,715 7,548,401 37,742,005

Collatz Trajectory (178 steps to reach 1)

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

37,742,005 113,226,016 56,613,008 28,306,504 14,153,252 7,076,626 3,538,313 10,614,940 5,307,470 2,653,735 7,961,206 3,980,603 11,941,810 5,970,905 17,912,716 8,956,358 4,478,179 13,434,538 6,717,269 20,151,808 10,075,904 5,037,952 2,518,976 1,259,488 629,744 314,872 157,436 78,718 39,359 118,078 59,039 177,118 88,559 265,678 132,839 398,518 199,259 597,778 298,889 896,668 448,334 224,167 672,502 336,251 1,008,754 504,377 1,513,132 756,566 378,283 1,134,850 567,425 1,702,276 851,138 425,569 1,276,708 638,354 319,177 957,532 478,766 239,383

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