λ
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Atlas › Integer Profiles › Node 7,641,592

7,641,592

23 × 7 × 61 × 2237
Abundant Even Composite

7,641,592 factors as 2^3 × 7 × 61 × 2237. Its 32 positive divisors give a proper-divisor sum of 9,009,128, so this integer is abundant. The Collatz stopping time is 129 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 61 × 2237
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 16,650,720
Proper Divisor Sum 9,009,128
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #7641533 ← → #7641611

Radix Representation

Decimal 7641592
Binary 11101001001100111111000 (23 bits)
Octal 0o35114770
Hexadecimal 0x7499F8

Divisor Catalog (32)

1 2 4 7 8 14 28 56 61 122 244 427 488 854 1,708 2,237 3,416 4,474 8,948 15,659 17,896 31,318 62,636 125,272 136,457 272,914 545,828 955,199 1,091,656 1,910,398 3,820,796 7,641,592

Collatz Trajectory (129 steps to reach 1)

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

7,641,592 3,820,796 1,910,398 955,199 2,865,598 1,432,799 4,298,398 2,149,199 6,447,598 3,223,799 9,671,398 4,835,699 14,507,098 7,253,549 21,760,648 10,880,324 5,440,162 2,720,081 8,160,244 4,080,122 2,040,061 6,120,184 3,060,092 1,530,046 765,023 2,295,070 1,147,535 3,442,606 1,721,303 5,163,910 2,581,955 7,745,866 3,872,933 11,618,800 5,809,400 2,904,700 1,452,350 726,175 2,178,526 1,089,263 3,267,790 1,633,895 4,901,686 2,450,843 7,352,530 3,676,265 11,028,796 5,514,398 2,757,199 8,271,598 4,135,799 12,407,398 6,203,699 18,611,098 9,305,549 27,916,648 13,958,324 6,979,162 3,489,581 10,468,744

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