7,736,391

3⁵ × 13 × 31 × 79

7,736,391 has digital root 9. The neighboring primes are 7736389 and 7736461; its proper-divisor sum differs from the starting integer by -2,427,022.

Prime Factor Structure

Factorization String 3^5 × 13 × 31 × 79

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 13,045,760

Proper Divisor Sum 5,309,369

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7736389 ← → #7736461

Radix Representation

Decimal	7736391
Binary	11101100000110001000111 (23 bits)
Octal	0o35406107
Hexadecimal	0x760C47

Divisor Catalog (48)

1 3 9 13 27 31 39 79 81 93 117 237 243 279 351 403 711 837 1,027 1,053 1,209 2,133 2,449 2,511 3,081 3,159 3,627 6,399 7,347 7,533 9,243 10,881 19,197 22,041 27,729 31,837 32,643 66,123 83,187 95,511 97,929 198,369 249,561 286,533 595,107 859,599 2,578,797 7,736,391

Collatz Trajectory (129 steps to reach 1)

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

7,736,391 23,209,174 11,604,587 34,813,762 17,406,881 52,220,644 26,110,322 13,055,161 39,165,484 19,582,742 9,791,371 29,374,114 14,687,057 44,061,172 22,030,586 11,015,293 33,045,880 16,522,940 8,261,470 4,130,735 12,392,206 6,196,103 18,588,310 9,294,155 27,882,466 13,941,233 41,823,700 20,911,850 10,455,925 31,367,776 15,683,888 7,841,944 3,920,972 1,960,486 980,243 2,940,730 1,470,365 4,411,096 2,205,548 1,102,774 551,387 1,654,162 827,081 2,481,244 1,240,622 620,311 1,860,934 930,467 2,791,402 1,395,701 4,187,104 2,093,552 1,046,776 523,388 261,694 130,847 392,542 196,271 588,814 294,407

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