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Atlas › Integer Profiles › Node 36,960,225

36,960,225

3 × 52 × 19 × 37 × 701
Deficient Odd Composite

36,960,225 factors as 3 × 5^2 × 19 × 37 × 701. Its 48 positive divisors give a proper-divisor sum of 29,196,255, so this integer is deficient. The Collatz stopping time is 134 steps.

Prime Factor Structure

Factorization String 3 × 5^2 × 19 × 37 × 701
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 66,156,480
Proper Divisor Sum 29,196,255
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #36960221 ← → #36960233

Radix Representation

Decimal 36960225
Binary 10001100111111011111100001 (26 bits)
Octal 0o214773741
Hexadecimal 0x233F7E1

Divisor Catalog (48)

1 3 5 15 19 25 37 57 75 95 111 185 285 475 555 701 703 925 1,425 2,103 2,109 2,775 3,505 3,515 10,515 10,545 13,319 17,525 17,575 25,937 39,957 52,575 52,725 66,595 77,811 129,685 199,785 332,975 389,055 492,803 648,425 998,925 1,478,409 1,945,275 2,464,015 7,392,045 12,320,075 36,960,225

Collatz Trajectory (134 steps to reach 1)

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

36,960,225 110,880,676 55,440,338 27,720,169 83,160,508 41,580,254 20,790,127 62,370,382 31,185,191 93,555,574 46,777,787 140,333,362 70,166,681 210,500,044 105,250,022 52,625,011 157,875,034 78,937,517 236,812,552 118,406,276 59,203,138 29,601,569 88,804,708 44,402,354 22,201,177 66,603,532 33,301,766 16,650,883 49,952,650 24,976,325 74,928,976 37,464,488 18,732,244 9,366,122 4,683,061 14,049,184 7,024,592 3,512,296 1,756,148 878,074 439,037 1,317,112 658,556 329,278 164,639 493,918 246,959 740,878 370,439 1,111,318 555,659 1,666,978 833,489 2,500,468 1,250,234 625,117 1,875,352 937,676 468,838 234,419

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