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Atlas › Integer Profiles › Node 36,927,114

36,927,114

2 × 3 × 7 × 532 × 313
Abundant Even Composite

36,927,114 factors as 2 × 3 × 7 × 53^2 × 313. Its 48 positive divisors give a proper-divisor sum of 49,375,158, so this integer is abundant. The Collatz stopping time is 77 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 53^2 × 313
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 86,302,272
Proper Divisor Sum 49,375,158
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #36927113 ← → #36927133

Radix Representation

Decimal 36927114
Binary 10001100110111011010001010 (26 bits)
Octal 0o214673212
Hexadecimal 0x233768A

Divisor Catalog (48)

1 2 3 6 7 14 21 42 53 106 159 313 318 371 626 742 939 1,113 1,878 2,191 2,226 2,809 4,382 5,618 6,573 8,427 13,146 16,589 16,854 19,663 33,178 39,326 49,767 58,989 99,534 116,123 117,978 232,246 348,369 696,738 879,217 1,758,434 2,637,651 5,275,302 6,154,519 12,309,038 18,463,557 36,927,114

Collatz Trajectory (77 steps to reach 1)

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

36,927,114 18,463,557 55,390,672 27,695,336 13,847,668 6,923,834 3,461,917 10,385,752 5,192,876 2,596,438 1,298,219 3,894,658 1,947,329 5,841,988 2,920,994 1,460,497 4,381,492 2,190,746 1,095,373 3,286,120 1,643,060 821,530 410,765 1,232,296 616,148 308,074 154,037 462,112 231,056 115,528 57,764 28,882 14,441 43,324 21,662 10,831 32,494 16,247 48,742 24,371 73,114 36,557 109,672 54,836 27,418 13,709 41,128 20,564 10,282 5,141 15,424 7,712 3,856 1,928 964 482 241 724 362 181

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