λ
Harmonic Matrix

7,808,199

3 × 72 × 53117
Deficient Odd Composite

7,808,199 has digital root 6. The neighboring primes are 7808197 and 7808231; its proper-divisor sum differs from the starting integer by -3,505,494.

Prime Factor Structure

Factorization String 3 × 7^2 × 53117
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 12,110,904
Proper Divisor Sum 4,302,705
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #7808197 ← → #7808231

Radix Representation

Decimal 7808199
Binary 11101110010010011000111 (23 bits)
Octal 0o35622307
Hexadecimal 0x7724C7

Divisor Catalog (12)

1 3 7 21 49 147 53,117 159,351 371,819 1,115,457 2,602,733 7,808,199

Collatz Trajectory (186 steps to reach 1)

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

7,808,199 23,424,598 11,712,299 35,136,898 17,568,449 52,705,348 26,352,674 13,176,337 39,529,012 19,764,506 9,882,253 29,646,760 14,823,380 7,411,690 3,705,845 11,117,536 5,558,768 2,779,384 1,389,692 694,846 347,423 1,042,270 521,135 1,563,406 781,703 2,345,110 1,172,555 3,517,666 1,758,833 5,276,500 2,638,250 1,319,125 3,957,376 1,978,688 989,344 494,672 247,336 123,668 61,834 30,917 92,752 46,376 23,188 11,594 5,797 17,392 8,696 4,348 2,174 1,087 3,262 1,631 4,894 2,447 7,342 3,671 11,014 5,507 16,522 8,261

More profiles

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