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Atlas › Integer Profiles › Node 7,127,964

7,127,964

22 × 32 × 17 × 19 × 613
Abundant Even Composite

7,127,964 factors as 2^2 × 3^2 × 17 × 19 × 613. Its 72 positive divisors give a proper-divisor sum of 12,986,676, so this integer is abundant. The Collatz stopping time is 121 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 17 × 19 × 613
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 20,114,640
Proper Divisor Sum 12,986,676
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #7127963 ← → #7127971

Radix Representation

Decimal 7127964
Binary 11011001100001110011100 (23 bits)
Octal 0o33141634
Hexadecimal 0x6CC39C

Divisor Catalog (60 of 72)

1 2 3 4 6 9 12 17 18 19 34 36 38 51 57 68 76 102 114 153 171 204 228 306 323 342 612 613 646 684 969 1,226 1,292 1,839 1,938 2,452 2,907 3,678 3,876 5,517 5,814 7,356 10,421 11,034 11,628 11,647 20,842 22,068 23,294 31,263 34,941 41,684 46,588 62,526 69,882 93,789 104,823 125,052 139,764 187,578

Collatz Trajectory (121 steps to reach 1)

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

7,127,964 3,563,982 1,781,991 5,345,974 2,672,987 8,018,962 4,009,481 12,028,444 6,014,222 3,007,111 9,021,334 4,510,667 13,532,002 6,766,001 20,298,004 10,149,002 5,074,501 15,223,504 7,611,752 3,805,876 1,902,938 951,469 2,854,408 1,427,204 713,602 356,801 1,070,404 535,202 267,601 802,804 401,402 200,701 602,104 301,052 150,526 75,263 225,790 112,895 338,686 169,343 508,030 254,015 762,046 381,023 1,143,070 571,535 1,714,606 857,303 2,571,910 1,285,955 3,857,866 1,928,933 5,786,800 2,893,400 1,446,700 723,350 361,675 1,085,026 542,513 1,627,540

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