7,840,065

3 × 5 × 19 × 27509

Starting at 7,840,065, the Collatz iteration reaches 1 after 93 steps. The first transition is 23520196; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 19 × 27509

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 13,204,800

Proper Divisor Sum 5,364,735

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7840057 ← → #7840067

Radix Representation

Decimal	7840065
Binary	11101111010000101000001 (23 bits)
Octal	0o35720501
Hexadecimal	0x77A141

Divisor Catalog (16)

1 3 5 15 19 57 95 285 27,509 82,527 137,545 412,635 522,671 1,568,013 2,613,355 7,840,065

Collatz Trajectory (93 steps to reach 1)

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

7,840,065 23,520,196 11,760,098 5,880,049 17,640,148 8,820,074 4,410,037 13,230,112 6,615,056 3,307,528 1,653,764 826,882 413,441 1,240,324 620,162 310,081 930,244 465,122 232,561 697,684 348,842 174,421 523,264 261,632 130,816 65,408 32,704 16,352 8,176 4,088 2,044 1,022 511 1,534 767 2,302 1,151 3,454 1,727 5,182 2,591 7,774 3,887 11,662 5,831 17,494 8,747 26,242 13,121 39,364 19,682 9,841 29,524 14,762 7,381 22,144 11,072 5,536 2,768 1,384

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