1,727,784

2³ × 3³ × 19 × 421

1,727,784 has digital root 9. The neighboring primes are 1727779 and 1727797; its proper-divisor sum differs from the starting integer by 1,608,432.

Prime Factor Structure

Factorization String 2^3 × 3^3 × 19 × 421

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 5,064,000

Proper Divisor Sum 3,336,216

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #1727779 ← → #1727797

Radix Representation

Decimal	1727784
Binary	110100101110100101000 (21 bits)
Octal	0o6456450
Hexadecimal	0x1A5D28

Divisor Catalog (60 of 64)

1 2 3 4 6 8 9 12 18 19 24 27 36 38 54 57 72 76 108 114 152 171 216 228 342 421 456 513 684 842 1,026 1,263 1,368 1,684 2,052 2,526 3,368 3,789 4,104 5,052 7,578 7,999 10,104 11,367 15,156 15,998 22,734 23,997 30,312 31,996 45,468 47,994 63,992 71,991 90,936 95,988 143,982 191,976 215,973 287,964

Collatz Trajectory (96 steps to reach 1)

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

1,727,784 863,892 431,946 215,973 647,920 323,960 161,980 80,990 40,495 121,486 60,743 182,230 91,115 273,346 136,673 410,020 205,010 102,505 307,516 153,758 76,879 230,638 115,319 345,958 172,979 518,938 259,469 778,408 389,204 194,602 97,301 291,904 145,952 72,976 36,488 18,244 9,122 4,561 13,684 6,842 3,421 10,264 5,132 2,566 1,283 3,850 1,925 5,776 2,888 1,444 722 361 1,084 542 271 814 407 1,222 611 1,834

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