7,852,664

2³ × 59 × 127 × 131

Starting at 7,852,664, the Collatz iteration reaches 1 after 155 steps. The first transition is 3926332; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 59 × 127 × 131

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 15,206,400

Proper Divisor Sum 7,353,736

Digit Sum / Digital Root 38 (Root: 2)

Adjacent Primes #7852661 ← → #7852711

Radix Representation

Decimal	7852664
Binary	11101111101001001111000 (23 bits)
Octal	0o35751170
Hexadecimal	0x77D278

Divisor Catalog (32)

1 2 4 8 59 118 127 131 236 254 262 472 508 524 1,016 1,048 7,493 7,729 14,986 15,458 16,637 29,972 30,916 33,274 59,944 61,832 66,548 133,096 981,583 1,963,166 3,926,332 7,852,664

Collatz Trajectory (155 steps to reach 1)

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

7,852,664 3,926,332 1,963,166 981,583 2,944,750 1,472,375 4,417,126 2,208,563 6,625,690 3,312,845 9,938,536 4,969,268 2,484,634 1,242,317 3,726,952 1,863,476 931,738 465,869 1,397,608 698,804 349,402 174,701 524,104 262,052 131,026 65,513 196,540 98,270 49,135 147,406 73,703 221,110 110,555 331,666 165,833 497,500 248,750 124,375 373,126 186,563 559,690 279,845 839,536 419,768 209,884 104,942 52,471 157,414 78,707 236,122 118,061 354,184 177,092 88,546 44,273 132,820 66,410 33,205 99,616 49,808

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