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Atlas › Integer Profiles › Node 72,561,940

72,561,940

22 × 5 × 11 × 61 × 5407
Abundant Even Composite

72,561,940 factors as 2^2 × 5 × 11 × 61 × 5407. Its 48 positive divisors give a proper-divisor sum of 96,427,244, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 11 × 61 × 5407
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 168,989,184
Proper Divisor Sum 96,427,244
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #72561911 ← → #72561977

Radix Representation

Decimal 72561940
Binary 100010100110011010100010100 (27 bits)
Octal 0o424632424
Hexadecimal 0x4533514

Divisor Catalog (48)

1 2 4 5 10 11 20 22 44 55 61 110 122 220 244 305 610 671 1,220 1,342 2,684 3,355 5,407 6,710 10,814 13,420 21,628 27,035 54,070 59,477 108,140 118,954 237,908 297,385 329,827 594,770 659,654 1,189,540 1,319,308 1,649,135 3,298,270 3,628,097 6,596,540 7,256,194 14,512,388 18,140,485 36,280,970 72,561,940

Collatz Trajectory (135 steps to reach 1)

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

72,561,940 36,280,970 18,140,485 54,421,456 27,210,728 13,605,364 6,802,682 3,401,341 10,204,024 5,102,012 2,551,006 1,275,503 3,826,510 1,913,255 5,739,766 2,869,883 8,609,650 4,304,825 12,914,476 6,457,238 3,228,619 9,685,858 4,842,929 14,528,788 7,264,394 3,632,197 10,896,592 5,448,296 2,724,148 1,362,074 681,037 2,043,112 1,021,556 510,778 255,389 766,168 383,084 191,542 95,771 287,314 143,657 430,972 215,486 107,743 323,230 161,615 484,846 242,423 727,270 363,635 1,090,906 545,453 1,636,360 818,180 409,090 204,545 613,636 306,818 153,409 460,228

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