λ
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Atlas › Integer Profiles › Node 36,955,940

36,955,940

22 × 5 × 7 × 232 × 499
Abundant Even Composite

36,955,940 factors as 2^2 × 5 × 7 × 23^2 × 499. Its 72 positive divisors give a proper-divisor sum of 55,948,060, so this integer is abundant. The Collatz stopping time is 134 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 23^2 × 499
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 92,904,000
Proper Divisor Sum 55,948,060
Digit Sum / Digital Root 41 (Root: 5)
Adjacent Primes #36955939 ← → #36955967

Radix Representation

Decimal 36955940
Binary 10001100111110011100100100 (26 bits)
Octal 0o214763444
Hexadecimal 0x233E724

Divisor Catalog (60 of 72)

1 2 4 5 7 10 14 20 23 28 35 46 70 92 115 140 161 230 322 460 499 529 644 805 998 1,058 1,610 1,996 2,116 2,495 2,645 3,220 3,493 3,703 4,990 5,290 6,986 7,406 9,980 10,580 11,477 13,972 14,812 17,465 18,515 22,954 34,930 37,030 45,908 57,385 69,860 74,060 80,339 114,770 160,678 229,540 263,971 321,356 401,695 527,942

Collatz Trajectory (134 steps to reach 1)

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

36,955,940 18,477,970 9,238,985 27,716,956 13,858,478 6,929,239 20,787,718 10,393,859 31,181,578 15,590,789 46,772,368 23,386,184 11,693,092 5,846,546 2,923,273 8,769,820 4,384,910 2,192,455 6,577,366 3,288,683 9,866,050 4,933,025 14,799,076 7,399,538 3,699,769 11,099,308 5,549,654 2,774,827 8,324,482 4,162,241 12,486,724 6,243,362 3,121,681 9,365,044 4,682,522 2,341,261 7,023,784 3,511,892 1,755,946 877,973 2,633,920 1,316,960 658,480 329,240 164,620 82,310 41,155 123,466 61,733 185,200 92,600 46,300 23,150 11,575 34,726 17,363 52,090 26,045 78,136 39,068

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