Harmonic Matrix

6,120,961

7 × 11 × 79493

6,120,961 has digital root 7. The neighboring primes are 6120949 and 6120971; its proper-divisor sum differs from the starting integer by -4,610,498.

Prime Factor Structure

Factorization String 7 × 11 × 79493

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 7,631,424

Proper Divisor Sum 1,510,463

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #6120949 ← → #6120971

Radix Representation

Decimal	6120961
Binary	10111010110011000000001 (23 bits)
Octal	0o27263001
Hexadecimal	0x5D6601

Divisor Catalog (8)

1 7 11 77 79,493 556,451 874,423 6,120,961

Collatz Trajectory (240 steps to reach 1)

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

6,120,961 18,362,884 9,181,442 4,590,721 13,772,164 6,886,082 3,443,041 10,329,124 5,164,562 2,582,281 7,746,844 3,873,422 1,936,711 5,810,134 2,905,067 8,715,202 4,357,601 13,072,804 6,536,402 3,268,201 9,804,604 4,902,302 2,451,151 7,353,454 3,676,727 11,030,182 5,515,091 16,545,274 8,272,637 24,817,912 12,408,956 6,204,478 3,102,239 9,306,718 4,653,359 13,960,078 6,980,039 20,940,118 10,470,059 31,410,178 15,705,089 47,115,268 23,557,634 11,778,817 35,336,452 17,668,226 8,834,113 26,502,340 13,251,170 6,625,585 19,876,756 9,938,378 4,969,189 14,907,568 7,453,784 3,726,892 1,863,446 931,723 2,795,170 1,397,585

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