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Atlas › Integer Profiles › Node 1,643,496

1,643,496

23 × 3 × 31 × 472
Abundant Even Composite

1,643,496 factors as 2^3 × 3 × 31 × 47^2. Its 48 positive divisors give a proper-divisor sum of 2,689,944, so this integer is abundant. The Collatz stopping time is 313 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 31 × 47^2
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 4,333,440
Proper Divisor Sum 2,689,944
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #1643491 ← → #1643497

Radix Representation

Decimal 1643496
Binary 110010001001111101000 (21 bits)
Octal 0o6211750
Hexadecimal 0x1913E8

Divisor Catalog (48)

1 2 3 4 6 8 12 24 31 47 62 93 94 124 141 186 188 248 282 372 376 564 744 1,128 1,457 2,209 2,914 4,371 4,418 5,828 6,627 8,742 8,836 11,656 13,254 17,484 17,672 26,508 34,968 53,016 68,479 136,958 205,437 273,916 410,874 547,832 821,748 1,643,496

Collatz Trajectory (313 steps to reach 1)

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

1,643,496 821,748 410,874 205,437 616,312 308,156 154,078 77,039 231,118 115,559 346,678 173,339 520,018 260,009 780,028 390,014 195,007 585,022 292,511 877,534 438,767 1,316,302 658,151 1,974,454 987,227 2,961,682 1,480,841 4,442,524 2,221,262 1,110,631 3,331,894 1,665,947 4,997,842 2,498,921 7,496,764 3,748,382 1,874,191 5,622,574 2,811,287 8,433,862 4,216,931 12,650,794 6,325,397 18,976,192 9,488,096 4,744,048 2,372,024 1,186,012 593,006 296,503 889,510 444,755 1,334,266 667,133 2,001,400 1,000,700 500,350 250,175 750,526 375,263

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