λ
Harmonic Matrix

3,173,823

35 × 37 × 353
Deficient Odd Composite

3,173,823 has digital root 9. The neighboring primes are 3173813 and 3173887; its proper-divisor sum differs from the starting integer by -1,451,118.

Prime Factor Structure

Factorization String 3^5 × 37 × 353
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 4,896,528
Proper Divisor Sum 1,722,705
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #3173813 ← → #3173887

Radix Representation

Decimal 3173823
Binary 1100000110110110111111 (22 bits)
Octal 0o14066677
Hexadecimal 0x306DBF

Divisor Catalog (24)

1 3 9 27 37 81 111 243 333 353 999 1,059 2,997 3,177 8,991 9,531 13,061 28,593 39,183 85,779 117,549 352,647 1,057,941 3,173,823

Collatz Trajectory (151 steps to reach 1)

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

3,173,823 9,521,470 4,760,735 14,282,206 7,141,103 21,423,310 10,711,655 32,134,966 16,067,483 48,202,450 24,101,225 72,303,676 36,151,838 18,075,919 54,227,758 27,113,879 81,341,638 40,670,819 122,012,458 61,006,229 183,018,688 91,509,344 45,754,672 22,877,336 11,438,668 5,719,334 2,859,667 8,579,002 4,289,501 12,868,504 6,434,252 3,217,126 1,608,563 4,825,690 2,412,845 7,238,536 3,619,268 1,809,634 904,817 2,714,452 1,357,226 678,613 2,035,840 1,017,920 508,960 254,480 127,240 63,620 31,810 15,905 47,716 23,858 11,929 35,788 17,894 8,947 26,842 13,421 40,264 20,132

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