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Atlas › Integer Profiles › Node 37,565,720

37,565,720

23 × 5 × 113 × 8311
Abundant Even Composite

37,565,720 factors as 2^3 × 5 × 113 × 8311. Its 32 positive divisors give a proper-divisor sum of 47,715,400, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 113 × 8311
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 85,281,120
Proper Divisor Sum 47,715,400
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #37565687 ← → #37565747

Radix Representation

Decimal 37565720
Binary 10001111010011010100011000 (26 bits)
Octal 0o217232430
Hexadecimal 0x23D3518

Divisor Catalog (32)

1 2 4 5 8 10 20 40 113 226 452 565 904 1,130 2,260 4,520 8,311 16,622 33,244 41,555 66,488 83,110 166,220 332,440 939,143 1,878,286 3,756,572 4,695,715 7,513,144 9,391,430 18,782,860 37,565,720

Collatz Trajectory (196 steps to reach 1)

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

37,565,720 18,782,860 9,391,430 4,695,715 14,087,146 7,043,573 21,130,720 10,565,360 5,282,680 2,641,340 1,320,670 660,335 1,981,006 990,503 2,971,510 1,485,755 4,457,266 2,228,633 6,685,900 3,342,950 1,671,475 5,014,426 2,507,213 7,521,640 3,760,820 1,880,410 940,205 2,820,616 1,410,308 705,154 352,577 1,057,732 528,866 264,433 793,300 396,650 198,325 594,976 297,488 148,744 74,372 37,186 18,593 55,780 27,890 13,945 41,836 20,918 10,459 31,378 15,689 47,068 23,534 11,767 35,302 17,651 52,954 26,477 79,432 39,716

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