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Atlas › Integer Profiles › Node 45,727,240

45,727,240

23 × 5 × 13 × 47 × 1871
Abundant Even Composite

45,727,240 factors as 2^3 × 5 × 13 × 47 × 1871. Its 64 positive divisors give a proper-divisor sum of 67,491,320, so this integer is abundant. The Collatz stopping time is 204 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 13 × 47 × 1871
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 113,218,560
Proper Divisor Sum 67,491,320
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #45727217 ← → #45727261

Radix Representation

Decimal 45727240
Binary 10101110011011111000001000 (26 bits)
Octal 0o256337010
Hexadecimal 0x2B9BE08

Divisor Catalog (60 of 64)

1 2 4 5 8 10 13 20 26 40 47 52 65 94 104 130 188 235 260 376 470 520 611 940 1,222 1,871 1,880 2,444 3,055 3,742 4,888 6,110 7,484 9,355 12,220 14,968 18,710 24,323 24,440 37,420 48,646 74,840 87,937 97,292 121,615 175,874 194,584 243,230 351,748 439,685 486,460 703,496 879,370 972,920 1,143,181 1,758,740 2,286,362 3,517,480 4,572,724 5,715,905

Collatz Trajectory (204 steps to reach 1)

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

45,727,240 22,863,620 11,431,810 5,715,905 17,147,716 8,573,858 4,286,929 12,860,788 6,430,394 3,215,197 9,645,592 4,822,796 2,411,398 1,205,699 3,617,098 1,808,549 5,425,648 2,712,824 1,356,412 678,206 339,103 1,017,310 508,655 1,525,966 762,983 2,288,950 1,144,475 3,433,426 1,716,713 5,150,140 2,575,070 1,287,535 3,862,606 1,931,303 5,793,910 2,896,955 8,690,866 4,345,433 13,036,300 6,518,150 3,259,075 9,777,226 4,888,613 14,665,840 7,332,920 3,666,460 1,833,230 916,615 2,749,846 1,374,923 4,124,770 2,062,385 6,187,156 3,093,578 1,546,789 4,640,368 2,320,184 1,160,092 580,046 290,023

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