7,825,527

3² × 43 × 73 × 277

Starting at 7,825,527, the Collatz iteration reaches 1 after 217 steps. The first transition is 23476582; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 43 × 73 × 277

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 11,767,184

Proper Divisor Sum 3,941,657

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7825523 ← → #7825529

Radix Representation

Decimal	7825527
Binary	11101110110100001110111 (23 bits)
Octal	0o35664167
Hexadecimal	0x776877

Divisor Catalog (24)

1 3 9 43 73 129 219 277 387 657 831 2,493 3,139 9,417 11,911 20,221 28,251 35,733 60,663 107,199 181,989 869,503 2,608,509 7,825,527

Collatz Trajectory (217 steps to reach 1)

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

7,825,527 23,476,582 11,738,291 35,214,874 17,607,437 52,822,312 26,411,156 13,205,578 6,602,789 19,808,368 9,904,184 4,952,092 2,476,046 1,238,023 3,714,070 1,857,035 5,571,106 2,785,553 8,356,660 4,178,330 2,089,165 6,267,496 3,133,748 1,566,874 783,437 2,350,312 1,175,156 587,578 293,789 881,368 440,684 220,342 110,171 330,514 165,257 495,772 247,886 123,943 371,830 185,915 557,746 278,873 836,620 418,310 209,155 627,466 313,733 941,200 470,600 235,300 117,650 58,825 176,476 88,238 44,119 132,358 66,179 198,538 99,269 297,808

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