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Atlas › Integer Profiles › Node 10,039,952

10,039,952

24 × 132 × 47 × 79
Abundant Even Composite

10,039,952 factors as 2^4 × 13^2 × 47 × 79. Its 60 positive divisors give a proper-divisor sum of 11,744,368, so this integer is abundant. The Collatz stopping time is 132 steps.

Prime Factor Structure

Factorization String 2^4 × 13^2 × 47 × 79
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 21,784,320
Proper Divisor Sum 11,744,368
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #10039951 ← → #10039963

Radix Representation

Decimal 10039952
Binary 100110010011001010010000 (24 bits)
Octal 0o46231220
Hexadecimal 0x993290

Divisor Catalog (60)

1 2 4 8 13 16 26 47 52 79 94 104 158 169 188 208 316 338 376 611 632 676 752 1,027 1,222 1,264 1,352 2,054 2,444 2,704 3,713 4,108 4,888 7,426 7,943 8,216 9,776 13,351 14,852 15,886 16,432 26,702 29,704 31,772 48,269 53,404 59,408 63,544 96,538 106,808 127,088 193,076 213,616 386,152 627,497 772,304 1,254,994 2,509,988 5,019,976 10,039,952

Collatz Trajectory (132 steps to reach 1)

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

10,039,952 5,019,976 2,509,988 1,254,994 627,497 1,882,492 941,246 470,623 1,411,870 705,935 2,117,806 1,058,903 3,176,710 1,588,355 4,765,066 2,382,533 7,147,600 3,573,800 1,786,900 893,450 446,725 1,340,176 670,088 335,044 167,522 83,761 251,284 125,642 62,821 188,464 94,232 47,116 23,558 11,779 35,338 17,669 53,008 26,504 13,252 6,626 3,313 9,940 4,970 2,485 7,456 3,728 1,864 932 466 233 700 350 175 526 263 790 395 1,186 593 1,780

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