7,837,713

3² × 13² × 5153

7,837,713 factors as 3^2 × 13^2 × 5153. Its 18 positive divisors give a proper-divisor sum of 4,423,653, so this integer is deficient. The Collatz stopping time is 186 steps.

Prime Factor Structure

Factorization String 3^2 × 13^2 × 5153

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 18

Divisor Sum (σ) 12,261,366

Proper Divisor Sum 4,423,653

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7837703 ← → #7837717

Radix Representation

Decimal	7837713
Binary	11101111001100000010001 (23 bits)
Octal	0o35714021
Hexadecimal	0x779811

Divisor Catalog (18)

1 3 9 13 39 117 169 507 1,521 5,153 15,459 46,377 66,989 200,967 602,901 870,857 2,612,571 7,837,713

Collatz Trajectory (186 steps to reach 1)

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

7,837,713 23,513,140 11,756,570 5,878,285 17,634,856 8,817,428 4,408,714 2,204,357 6,613,072 3,306,536 1,653,268 826,634 413,317 1,239,952 619,976 309,988 154,994 77,497 232,492 116,246 58,123 174,370 87,185 261,556 130,778 65,389 196,168 98,084 49,042 24,521 73,564 36,782 18,391 55,174 27,587 82,762 41,381 124,144 62,072 31,036 15,518 7,759 23,278 11,639 34,918 17,459 52,378 26,189 78,568 39,284 19,642 9,821 29,464 14,732 7,366 3,683 11,050 5,525 16,576 8,288

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