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Atlas › Integer Profiles › Node 41,006,406

41,006,406

2 × 3 × 7 × 29 × 131 × 257
Abundant Even Composite

41,006,406 factors as 2 × 3 × 7 × 29 × 131 × 257. Its 64 positive divisors give a proper-divisor sum of 57,074,874, so this integer is abundant. The Collatz stopping time is 253 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 29 × 131 × 257
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 98,081,280
Proper Divisor Sum 57,074,874
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #41006387 ← → #41006461

Radix Representation

Decimal 41006406
Binary 10011100011011010101000110 (26 bits)
Octal 0o234332506
Hexadecimal 0x271B546

Divisor Catalog (60 of 64)

1 2 3 6 7 14 21 29 42 58 87 131 174 203 257 262 393 406 514 609 771 786 917 1,218 1,542 1,799 1,834 2,751 3,598 3,799 5,397 5,502 7,453 7,598 10,794 11,397 14,906 22,359 22,794 26,593 33,667 44,718 52,171 53,186 67,334 79,779 101,001 104,342 156,513 159,558 202,002 235,669 313,026 471,338 707,007 976,343 1,414,014 1,952,686 2,929,029 5,858,058

Collatz Trajectory (253 steps to reach 1)

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

41,006,406 20,503,203 61,509,610 30,754,805 92,264,416 46,132,208 23,066,104 11,533,052 5,766,526 2,883,263 8,649,790 4,324,895 12,974,686 6,487,343 19,462,030 9,731,015 29,193,046 14,596,523 43,789,570 21,894,785 65,684,356 32,842,178 16,421,089 49,263,268 24,631,634 12,315,817 36,947,452 18,473,726 9,236,863 27,710,590 13,855,295 41,565,886 20,782,943 62,348,830 31,174,415 93,523,246 46,761,623 140,284,870 70,142,435 210,427,306 105,213,653 315,640,960 157,820,480 78,910,240 39,455,120 19,727,560 9,863,780 4,931,890 2,465,945 7,397,836 3,698,918 1,849,459 5,548,378 2,774,189 8,322,568 4,161,284 2,080,642 1,040,321 3,120,964 1,560,482

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