λ
Harmonic Matrix

7,650,097

7 × 13 × 84067
Deficient Odd Composite

7,650,097 has digital root 7. The neighboring primes are 7650077 and 7650121; its proper-divisor sum differs from the starting integer by -5,884,578.

Prime Factor Structure

Factorization String 7 × 13 × 84067
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 9,415,616
Proper Divisor Sum 1,765,519
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #7650077 ← → #7650121

Radix Representation

Decimal 7650097
Binary 11101001011101100110001 (23 bits)
Octal 0o35135461
Hexadecimal 0x74BB31

Divisor Catalog (8)

1 7 13 91 84,067 588,469 1,092,871 7,650,097

Collatz Trajectory (80 steps to reach 1)

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

7,650,097 22,950,292 11,475,146 5,737,573 17,212,720 8,606,360 4,303,180 2,151,590 1,075,795 3,227,386 1,613,693 4,841,080 2,420,540 1,210,270 605,135 1,815,406 907,703 2,723,110 1,361,555 4,084,666 2,042,333 6,127,000 3,063,500 1,531,750 765,875 2,297,626 1,148,813 3,446,440 1,723,220 861,610 430,805 1,292,416 646,208 323,104 161,552 80,776 40,388 20,194 10,097 30,292 15,146 7,573 22,720 11,360 5,680 2,840 1,420 710 355 1,066 533 1,600 800 400 200 100 50 25 76 38

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