9,906,273

3³ × 13³ × 167

Starting at 9,906,273, the Collatz iteration reaches 1 after 194 steps. The first transition is 29718820; the starting value is odd with 32 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 13^3 × 167

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 15,993,600

Proper Divisor Sum 6,087,327

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #9906271 ← → #9906289

Radix Representation

Decimal	9906273
Binary	100101110010100001100001 (24 bits)
Octal	0o45624141
Hexadecimal	0x972861

Divisor Catalog (32)

1 3 9 13 27 39 117 167 169 351 501 507 1,503 1,521 2,171 2,197 4,509 4,563 6,513 6,591 19,539 19,773 28,223 58,617 59,319 84,669 254,007 366,899 762,021 1,100,697 3,302,091 9,906,273

Collatz Trajectory (194 steps to reach 1)

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

9,906,273 29,718,820 14,859,410 7,429,705 22,289,116 11,144,558 5,572,279 16,716,838 8,358,419 25,075,258 12,537,629 37,612,888 18,806,444 9,403,222 4,701,611 14,104,834 7,052,417 21,157,252 10,578,626 5,289,313 15,867,940 7,933,970 3,966,985 11,900,956 5,950,478 2,975,239 8,925,718 4,462,859 13,388,578 6,694,289 20,082,868 10,041,434 5,020,717 15,062,152 7,531,076 3,765,538 1,882,769 5,648,308 2,824,154 1,412,077 4,236,232 2,118,116 1,059,058 529,529 1,588,588 794,294 397,147 1,191,442 595,721 1,787,164 893,582 446,791 1,340,374 670,187 2,010,562 1,005,281 3,015,844 1,507,922 753,961 2,261,884

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