405,223

7 × 13 × 61 × 73

Starting at 405,223, the Collatz iteration reaches 1 after 86 steps. The first transition is 1215670; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 7 × 13 × 61 × 73

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 513,856

Proper Divisor Sum 108,633

Digit Sum / Digital Root 16 (Root: 7)

Adjacent Primes #405221 ← → #405227

Radix Representation

Decimal	405223
Binary	1100010111011100111 (19 bits)
Octal	0o1427347
Hexadecimal	0x62EE7

Divisor Catalog (16)

1 7 13 61 73 91 427 511 793 949 4,453 5,551 6,643 31,171 57,889 405,223

Collatz Trajectory (86 steps to reach 1)

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

405,223 1,215,670 607,835 1,823,506 911,753 2,735,260 1,367,630 683,815 2,051,446 1,025,723 3,077,170 1,538,585 4,615,756 2,307,878 1,153,939 3,461,818 1,730,909 5,192,728 2,596,364 1,298,182 649,091 1,947,274 973,637 2,920,912 1,460,456 730,228 365,114 182,557 547,672 273,836 136,918 68,459 205,378 102,689 308,068 154,034 77,017 231,052 115,526 57,763 173,290 86,645 259,936 129,968 64,984 32,492 16,246 8,123 24,370 12,185 36,556 18,278 9,139 27,418 13,709 41,128 20,564 10,282 5,141 15,424

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