13,680,342

2 × 3² × 13 × 17 × 19 × 181

13,680,342 factors as 2 × 3^2 × 13 × 17 × 19 × 181. Its 96 positive divisors give a proper-divisor sum of 22,093,578, so this integer is abundant. The Collatz stopping time is 130 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 13 × 17 × 19 × 181

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 35,773,920

Proper Divisor Sum 22,093,578

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #13680341 ← → #13680353

Radix Representation

Decimal	13680342
Binary	110100001011111011010110 (24 bits)
Octal	0o64137326
Hexadecimal	0xD0BED6

Divisor Catalog (60 of 96)

1 2 3 6 9 13 17 18 19 26 34 38 39 51 57 78 102 114 117 153 171 181 221 234 247 306 323 342 362 442 494 543 646 663 741 969 1,086 1,326 1,482 1,629 1,938 1,989 2,223 2,353 2,907 3,077 3,258 3,439 3,978 4,199 4,446 4,706 5,814 6,154 6,878 7,059 8,398 9,231 10,317 12,597

Collatz Trajectory (130 steps to reach 1)

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

13,680,342 6,840,171 20,520,514 10,260,257 30,780,772 15,390,386 7,695,193 23,085,580 11,542,790 5,771,395 17,314,186 8,657,093 25,971,280 12,985,640 6,492,820 3,246,410 1,623,205 4,869,616 2,434,808 1,217,404 608,702 304,351 913,054 456,527 1,369,582 684,791 2,054,374 1,027,187 3,081,562 1,540,781 4,622,344 2,311,172 1,155,586 577,793 1,733,380 866,690 433,345 1,300,036 650,018 325,009 975,028 487,514 243,757 731,272 365,636 182,818 91,409 274,228 137,114 68,557 205,672 102,836 51,418 25,709 77,128 38,564 19,282 9,641 28,924 14,462

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