λ
Harmonic Matrix

8,476,075

52 × 23 × 14741
Deficient Odd Composite

8,476,075 has digital root 1. The neighboring primes are 8476073 and 8476079; its proper-divisor sum differs from the starting integer by -5,984,102.

Prime Factor Structure

Factorization String 5^2 × 23 × 14741
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 10,968,048
Proper Divisor Sum 2,491,973
Digit Sum / Digital Root 37 (Root: 1)
Adjacent Primes #8476073 ← → #8476079

Radix Representation

Decimal 8476075
Binary 100000010101010110101011 (24 bits)
Octal 0o40252653
Hexadecimal 0x8155AB

Divisor Catalog (12)

1 5 23 25 115 575 14,741 73,705 339,043 368,525 1,695,215 8,476,075

Collatz Trajectory (186 steps to reach 1)

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

8,476,075 25,428,226 12,714,113 38,142,340 19,071,170 9,535,585 28,606,756 14,303,378 7,151,689 21,455,068 10,727,534 5,363,767 16,091,302 8,045,651 24,136,954 12,068,477 36,205,432 18,102,716 9,051,358 4,525,679 13,577,038 6,788,519 20,365,558 10,182,779 30,548,338 15,274,169 45,822,508 22,911,254 11,455,627 34,366,882 17,183,441 51,550,324 25,775,162 12,887,581 38,662,744 19,331,372 9,665,686 4,832,843 14,498,530 7,249,265 21,747,796 10,873,898 5,436,949 16,310,848 8,155,424 4,077,712 2,038,856 1,019,428 509,714 254,857 764,572 382,286 191,143 573,430 286,715 860,146 430,073 1,290,220 645,110 322,555

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