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Atlas › Integer Profiles › Node 6,497,972

6,497,972

22 × 13 × 29 × 31 × 139
Abundant Even Composite

6,497,972 factors as 2^2 × 13 × 29 × 31 × 139. Its 48 positive divisors give a proper-divisor sum of 6,673,228, so this integer is abundant. The Collatz stopping time is 103 steps.

Prime Factor Structure

Factorization String 2^2 × 13 × 29 × 31 × 139
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 13,171,200
Proper Divisor Sum 6,673,228
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #6497969 ← → #6497989

Radix Representation

Decimal 6497972
Binary 11000110010011010110100 (23 bits)
Octal 0o30623264
Hexadecimal 0x6326B4

Divisor Catalog (48)

1 2 4 13 26 29 31 52 58 62 116 124 139 278 377 403 556 754 806 899 1,508 1,612 1,798 1,807 3,596 3,614 4,031 4,309 7,228 8,062 8,618 11,687 16,124 17,236 23,374 46,748 52,403 56,017 104,806 112,034 124,961 209,612 224,068 249,922 499,844 1,624,493 3,248,986 6,497,972

Collatz Trajectory (103 steps to reach 1)

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

6,497,972 3,248,986 1,624,493 4,873,480 2,436,740 1,218,370 609,185 1,827,556 913,778 456,889 1,370,668 685,334 342,667 1,028,002 514,001 1,542,004 771,002 385,501 1,156,504 578,252 289,126 144,563 433,690 216,845 650,536 325,268 162,634 81,317 243,952 121,976 60,988 30,494 15,247 45,742 22,871 68,614 34,307 102,922 51,461 154,384 77,192 38,596 19,298 9,649 28,948 14,474 7,237 21,712 10,856 5,428 2,714 1,357 4,072 2,036 1,018 509 1,528 764 382 191

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