7,762,516

2² × 601 × 3229

Starting at 7,762,516, the Collatz iteration reaches 1 after 217 steps. The first transition is 3881258; the starting value is even with 12 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 601 × 3229

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 13,611,220

Proper Divisor Sum 5,848,704

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #7762511 ← → #7762537

Radix Representation

Decimal	7762516
Binary	11101100111001001010100 (23 bits)
Octal	0o35471124
Hexadecimal	0x767254

Divisor Catalog (12)

1 2 4 601 1,202 2,404 3,229 6,458 12,916 1,940,629 3,881,258 7,762,516

Collatz Trajectory (217 steps to reach 1)

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

7,762,516 3,881,258 1,940,629 5,821,888 2,910,944 1,455,472 727,736 363,868 181,934 90,967 272,902 136,451 409,354 204,677 614,032 307,016 153,508 76,754 38,377 115,132 57,566 28,783 86,350 43,175 129,526 64,763 194,290 97,145 291,436 145,718 72,859 218,578 109,289 327,868 163,934 81,967 245,902 122,951 368,854 184,427 553,282 276,641 829,924 414,962 207,481 622,444 311,222 155,611 466,834 233,417 700,252 350,126 175,063 525,190 262,595 787,786 393,893 1,181,680 590,840 295,420

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