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Atlas › Integer Profiles › Node 36,944,136

36,944,136

23 × 32 × 263 × 1951
Abundant Even Composite

36,944,136 factors as 2^3 × 3^2 × 263 × 1951. Its 48 positive divisors give a proper-divisor sum of 63,544,824, so this integer is abundant. The Collatz stopping time is 121 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 263 × 1951
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 100,488,960
Proper Divisor Sum 63,544,824
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #36944129 ← → #36944137

Radix Representation

Decimal 36944136
Binary 10001100111011100100001000 (26 bits)
Octal 0o214734410
Hexadecimal 0x233B908

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 72 263 526 789 1,052 1,578 1,951 2,104 2,367 3,156 3,902 4,734 5,853 6,312 7,804 9,468 11,706 15,608 17,559 18,936 23,412 35,118 46,824 70,236 140,472 513,113 1,026,226 1,539,339 2,052,452 3,078,678 4,104,904 4,618,017 6,157,356 9,236,034 12,314,712 18,472,068 36,944,136

Collatz Trajectory (121 steps to reach 1)

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

36,944,136 18,472,068 9,236,034 4,618,017 13,854,052 6,927,026 3,463,513 10,390,540 5,195,270 2,597,635 7,792,906 3,896,453 11,689,360 5,844,680 2,922,340 1,461,170 730,585 2,191,756 1,095,878 547,939 1,643,818 821,909 2,465,728 1,232,864 616,432 308,216 154,108 77,054 38,527 115,582 57,791 173,374 86,687 260,062 130,031 390,094 195,047 585,142 292,571 877,714 438,857 1,316,572 658,286 329,143 987,430 493,715 1,481,146 740,573 2,221,720 1,110,860 555,430 277,715 833,146 416,573 1,249,720 624,860 312,430 156,215 468,646 234,323

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