λ
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Atlas › Integer Profiles › Node 27,927,970

27,927,970

2 × 5 × 7 × 37 × 41 × 263
Abundant Even Composite

27,927,970 factors as 2 × 5 × 7 × 37 × 41 × 263. Its 64 positive divisors give a proper-divisor sum of 32,745,566, so this integer is abundant. The Collatz stopping time is 162 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 37 × 41 × 263
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 60,673,536
Proper Divisor Sum 32,745,566
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #27927961 ← → #27927973

Radix Representation

Decimal 27927970
Binary 1101010100010010110100010 (25 bits)
Octal 0o152422642
Hexadecimal 0x1AA25A2

Divisor Catalog (60 of 64)

1 2 5 7 10 14 35 37 41 70 74 82 185 205 259 263 287 370 410 518 526 574 1,295 1,315 1,435 1,517 1,841 2,590 2,630 2,870 3,034 3,682 7,585 9,205 9,731 10,619 10,783 15,170 18,410 19,462 21,238 21,566 48,655 53,095 53,915 68,117 75,481 97,310 106,190 107,830 136,234 150,962 340,585 377,405 398,971 681,170 754,810 797,942 1,994,855 2,792,797

Collatz Trajectory (162 steps to reach 1)

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

27,927,970 13,963,985 41,891,956 20,945,978 10,472,989 31,418,968 15,709,484 7,854,742 3,927,371 11,782,114 5,891,057 17,673,172 8,836,586 4,418,293 13,254,880 6,627,440 3,313,720 1,656,860 828,430 414,215 1,242,646 621,323 1,863,970 931,985 2,795,956 1,397,978 698,989 2,096,968 1,048,484 524,242 262,121 786,364 393,182 196,591 589,774 294,887 884,662 442,331 1,326,994 663,497 1,990,492 995,246 497,623 1,492,870 746,435 2,239,306 1,119,653 3,358,960 1,679,480 839,740 419,870 209,935 629,806 314,903 944,710 472,355 1,417,066 708,533 2,125,600 1,062,800

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