λ
Harmonic Matrix

8,355,005

5 × 307 × 5443
Deficient Odd Composite

8,355,005 has digital root 8. The neighboring primes are 8355001 and 8355013; its proper-divisor sum differs from the starting integer by -6,649,498.

Prime Factor Structure

Factorization String 5 × 307 × 5443
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 10,060,512
Proper Divisor Sum 1,705,507
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #8355001 ← → #8355013

Radix Representation

Decimal 8355005
Binary 11111110111110010111101 (23 bits)
Octal 0o37676275
Hexadecimal 0x7F7CBD

Divisor Catalog (8)

1 5 307 1,535 5,443 27,215 1,671,001 8,355,005

Collatz Trajectory (111 steps to reach 1)

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

8,355,005 25,065,016 12,532,508 6,266,254 3,133,127 9,399,382 4,699,691 14,099,074 7,049,537 21,148,612 10,574,306 5,287,153 15,861,460 7,930,730 3,965,365 11,896,096 5,948,048 2,974,024 1,487,012 743,506 371,753 1,115,260 557,630 278,815 836,446 418,223 1,254,670 627,335 1,882,006 941,003 2,823,010 1,411,505 4,234,516 2,117,258 1,058,629 3,175,888 1,587,944 793,972 396,986 198,493 595,480 297,740 148,870 74,435 223,306 111,653 334,960 167,480 83,740 41,870 20,935 62,806 31,403 94,210 47,105 141,316 70,658 35,329 105,988 52,994

More profiles

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