627,015

3 × 5 × 41801

Starting at 627,015, the Collatz iteration reaches 1 after 172 steps. The first transition is 1881046; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 41801

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 1,003,248

Proper Divisor Sum 376,233

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #626987 ← → #627017

Radix Representation

Decimal	627015
Binary	10011001000101000111 (20 bits)
Octal	0o2310507
Hexadecimal	0x99147

Divisor Catalog (8)

1 3 5 15 41,801 125,403 209,005 627,015

Collatz Trajectory (172 steps to reach 1)

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

627,015 1,881,046 940,523 2,821,570 1,410,785 4,232,356 2,116,178 1,058,089 3,174,268 1,587,134 793,567 2,380,702 1,190,351 3,571,054 1,785,527 5,356,582 2,678,291 8,034,874 4,017,437 12,052,312 6,026,156 3,013,078 1,506,539 4,519,618 2,259,809 6,779,428 3,389,714 1,694,857 5,084,572 2,542,286 1,271,143 3,813,430 1,906,715 5,720,146 2,860,073 8,580,220 4,290,110 2,145,055 6,435,166 3,217,583 9,652,750 4,826,375 14,479,126 7,239,563 21,718,690 10,859,345 32,578,036 16,289,018 8,144,509 24,433,528 12,216,764 6,108,382 3,054,191 9,162,574 4,581,287 13,743,862 6,871,931 20,615,794 10,307,897 30,923,692

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