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Atlas › Integer Profiles › Node 7,675,640

7,675,640

23 × 5 × 7 × 79 × 347
Abundant Even Composite

7,675,640 factors as 2^3 × 5 × 7 × 79 × 347. Its 64 positive divisors give a proper-divisor sum of 12,369,160, so this integer is abundant. The Collatz stopping time is 204 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 79 × 347
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 20,044,800
Proper Divisor Sum 12,369,160
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #7675637 ← → #7675649

Radix Representation

Decimal 7675640
Binary 11101010001111011111000 (23 bits)
Octal 0o35217370
Hexadecimal 0x751EF8

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 79 140 158 280 316 347 395 553 632 694 790 1,106 1,388 1,580 1,735 2,212 2,429 2,765 2,776 3,160 3,470 4,424 4,858 5,530 6,940 9,716 11,060 12,145 13,880 19,432 22,120 24,290 27,413 48,580 54,826 97,160 109,652 137,065 191,891 219,304 274,130 383,782 548,260 767,564 959,455 1,096,520

Collatz Trajectory (204 steps to reach 1)

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

7,675,640 3,837,820 1,918,910 959,455 2,878,366 1,439,183 4,317,550 2,158,775 6,476,326 3,238,163 9,714,490 4,857,245 14,571,736 7,285,868 3,642,934 1,821,467 5,464,402 2,732,201 8,196,604 4,098,302 2,049,151 6,147,454 3,073,727 9,221,182 4,610,591 13,831,774 6,915,887 20,747,662 10,373,831 31,121,494 15,560,747 46,682,242 23,341,121 70,023,364 35,011,682 17,505,841 52,517,524 26,258,762 13,129,381 39,388,144 19,694,072 9,847,036 4,923,518 2,461,759 7,385,278 3,692,639 11,077,918 5,538,959 16,616,878 8,308,439 24,925,318 12,462,659 37,387,978 18,693,989 56,081,968 28,040,984 14,020,492 7,010,246 3,505,123 10,515,370

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