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Atlas › Integer Profiles › Node 71,209,528

71,209,528

23 × 13 × 53 × 12919
Abundant Even Composite

71,209,528 factors as 2^3 × 13 × 53 × 12919. Its 32 positive divisors give a proper-divisor sum of 75,303,272, so this integer is abundant. The Collatz stopping time is 96 steps.

Prime Factor Structure

Factorization String 2^3 × 13 × 53 × 12919
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 146,512,800
Proper Divisor Sum 75,303,272
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #71209499 ← → #71209531

Radix Representation

Decimal 71209528
Binary 100001111101001001000111000 (27 bits)
Octal 0o417511070
Hexadecimal 0x43E9238

Divisor Catalog (32)

1 2 4 8 13 26 52 53 104 106 212 424 689 1,378 2,756 5,512 12,919 25,838 51,676 103,352 167,947 335,894 671,788 684,707 1,343,576 1,369,414 2,738,828 5,477,656 8,901,191 17,802,382 35,604,764 71,209,528

Collatz Trajectory (96 steps to reach 1)

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

71,209,528 35,604,764 17,802,382 8,901,191 26,703,574 13,351,787 40,055,362 20,027,681 60,083,044 30,041,522 15,020,761 45,062,284 22,531,142 11,265,571 33,796,714 16,898,357 50,695,072 25,347,536 12,673,768 6,336,884 3,168,442 1,584,221 4,752,664 2,376,332 1,188,166 594,083 1,782,250 891,125 2,673,376 1,336,688 668,344 334,172 167,086 83,543 250,630 125,315 375,946 187,973 563,920 281,960 140,980 70,490 35,245 105,736 52,868 26,434 13,217 39,652 19,826 9,913 29,740 14,870 7,435 22,306 11,153 33,460 16,730 8,365 25,096 12,548

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