65,527

7 × 11 × 23 × 37

Starting at 65,527, the Collatz iteration reaches 1 after 161 steps. The first transition is 196582; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 7 × 11 × 23 × 37

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 87,552

Proper Divisor Sum 22,025

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #65521 ← → #65537

Radix Representation

Decimal	65527
Binary	1111111111110111 (16 bits)
Octal	0o177767
Hexadecimal	0xFFF7

Divisor Catalog (16)

1 7 11 23 37 77 161 253 259 407 851 1,771 2,849 5,957 9,361 65,527

Collatz Trajectory (161 steps to reach 1)

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

65,527 196,582 98,291 294,874 147,437 442,312 221,156 110,578 55,289 165,868 82,934 41,467 124,402 62,201 186,604 93,302 46,651 139,954 69,977 209,932 104,966 52,483 157,450 78,725 236,176 118,088 59,044 29,522 14,761 44,284 22,142 11,071 33,214 16,607 49,822 24,911 74,734 37,367 112,102 56,051 168,154 84,077 252,232 126,116 63,058 31,529 94,588 47,294 23,647 70,942 35,471 106,414 53,207 159,622 79,811 239,434 119,717 359,152 179,576 89,788

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