409,676

2² × 23 × 61 × 73

Starting at 409,676, the Collatz iteration reaches 1 after 81 steps. The first transition is 204838; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 23 × 61 × 73

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 770,784

Proper Divisor Sum 361,108

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #409657 ← → #409691

Radix Representation

Decimal	409676
Binary	1100100000001001100 (19 bits)
Octal	0o1440114
Hexadecimal	0x6404C

Divisor Catalog (24)

1 2 4 23 46 61 73 92 122 146 244 292 1,403 1,679 2,806 3,358 4,453 5,612 6,716 8,906 17,812 102,419 204,838 409,676

Collatz Trajectory (81 steps to reach 1)

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

409,676 204,838 102,419 307,258 153,629 460,888 230,444 115,222 57,611 172,834 86,417 259,252 129,626 64,813 194,440 97,220 48,610 24,305 72,916 36,458 18,229 54,688 27,344 13,672 6,836 3,418 1,709 5,128 2,564 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814 407 1,222 611 1,834 917 2,752 1,376 688 344 172 86 43 130 65 196 98 49 148 74

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