λ
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Atlas › Integer Profiles › Node 84,752,540

84,752,540

22 × 5 × 19 × 271 × 823
Abundant Even Composite

84,752,540 factors as 2^2 × 5 × 19 × 271 × 823. Its 48 positive divisors give a proper-divisor sum of 103,514,980, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 19 × 271 × 823
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 188,267,520
Proper Divisor Sum 103,514,980
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #84752537 ← → #84752573

Radix Representation

Decimal 84752540
Binary 101000011010011100010011100 (27 bits)
Octal 0o503234234
Hexadecimal 0x50D389C

Divisor Catalog (48)

1 2 4 5 10 19 20 38 76 95 190 271 380 542 823 1,084 1,355 1,646 2,710 3,292 4,115 5,149 5,420 8,230 10,298 15,637 16,460 20,596 25,745 31,274 51,490 62,548 78,185 102,980 156,370 223,033 312,740 446,066 892,132 1,115,165 2,230,330 4,237,627 4,460,660 8,475,254 16,950,508 21,188,135 42,376,270 84,752,540

Collatz Trajectory (192 steps to reach 1)

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

84,752,540 42,376,270 21,188,135 63,564,406 31,782,203 95,346,610 47,673,305 143,019,916 71,509,958 35,754,979 107,264,938 53,632,469 160,897,408 80,448,704 40,224,352 20,112,176 10,056,088 5,028,044 2,514,022 1,257,011 3,771,034 1,885,517 5,656,552 2,828,276 1,414,138 707,069 2,121,208 1,060,604 530,302 265,151 795,454 397,727 1,193,182 596,591 1,789,774 894,887 2,684,662 1,342,331 4,026,994 2,013,497 6,040,492 3,020,246 1,510,123 4,530,370 2,265,185 6,795,556 3,397,778 1,698,889 5,096,668 2,548,334 1,274,167 3,822,502 1,911,251 5,733,754 2,866,877 8,600,632 4,300,316 2,150,158 1,075,079 3,225,238

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