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Atlas › Integer Profiles › Node 40,501,384

40,501,384

23 × 7 × 11 × 37 × 1777
Abundant Even Composite

40,501,384 factors as 2^3 × 7 × 11 × 37 × 1777. Its 64 positive divisors give a proper-divisor sum of 56,790,776, so this integer is abundant. The Collatz stopping time is 253 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 11 × 37 × 1777
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 97,292,160
Proper Divisor Sum 56,790,776
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #40501379 ← → #40501387

Radix Representation

Decimal 40501384
Binary 10011010100000000010001000 (26 bits)
Octal 0o232400210
Hexadecimal 0x26A0088

Divisor Catalog (60 of 64)

1 2 4 7 8 11 14 22 28 37 44 56 74 77 88 148 154 259 296 308 407 518 616 814 1,036 1,628 1,777 2,072 2,849 3,256 3,554 5,698 7,108 11,396 12,439 14,216 19,547 22,792 24,878 39,094 49,756 65,749 78,188 99,512 131,498 136,829 156,376 262,996 273,658 460,243 525,992 547,316 723,239 920,486 1,094,632 1,446,478 1,840,972 2,892,956 3,681,944 5,062,673

Collatz Trajectory (253 steps to reach 1)

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

40,501,384 20,250,692 10,125,346 5,062,673 15,188,020 7,594,010 3,797,005 11,391,016 5,695,508 2,847,754 1,423,877 4,271,632 2,135,816 1,067,908 533,954 266,977 800,932 400,466 200,233 600,700 300,350 150,175 450,526 225,263 675,790 337,895 1,013,686 506,843 1,520,530 760,265 2,280,796 1,140,398 570,199 1,710,598 855,299 2,565,898 1,282,949 3,848,848 1,924,424 962,212 481,106 240,553 721,660 360,830 180,415 541,246 270,623 811,870 405,935 1,217,806 608,903 1,826,710 913,355 2,740,066 1,370,033 4,110,100 2,055,050 1,027,525 3,082,576 1,541,288

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