503,480

2³ × 5 × 41 × 307

Starting at 503,480, the Collatz iteration reaches 1 after 89 steps. The first transition is 251740; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 41 × 307

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,164,240

Proper Divisor Sum 660,760

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #503453 ← → #503483

Radix Representation

Decimal	503480
Binary	1111010111010111000 (19 bits)
Octal	0o1727270
Hexadecimal	0x7AEB8

Divisor Catalog (32)

1 2 4 5 8 10 20 40 41 82 164 205 307 328 410 614 820 1,228 1,535 1,640 2,456 3,070 6,140 12,280 12,587 25,174 50,348 62,935 100,696 125,870 251,740 503,480

Collatz Trajectory (89 steps to reach 1)

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

503,480 251,740 125,870 62,935 188,806 94,403 283,210 141,605 424,816 212,408 106,204 53,102 26,551 79,654 39,827 119,482 59,741 179,224 89,612 44,806 22,403 67,210 33,605 100,816 50,408 25,204 12,602 6,301 18,904 9,452 4,726 2,363 7,090 3,545 10,636 5,318 2,659 7,978 3,989 11,968 5,984 2,992 1,496 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538

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