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Atlas › Integer Profiles › Node 46,522,640

46,522,640

24 × 5 × 19 × 127 × 241
Abundant Even Composite

46,522,640 factors as 2^4 × 5 × 19 × 127 × 241. Its 80 positive divisors give a proper-divisor sum of 68,708,080, so this integer is abundant. The Collatz stopping time is 217 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 19 × 127 × 241
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 115,230,720
Proper Divisor Sum 68,708,080
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #46522633 ← → #46522643

Radix Representation

Decimal 46522640
Binary 10110001011110000100010000 (26 bits)
Octal 0o261360420
Hexadecimal 0x2C5E110

Divisor Catalog (60 of 80)

1 2 4 5 8 10 16 19 20 38 40 76 80 95 127 152 190 241 254 304 380 482 508 635 760 964 1,016 1,205 1,270 1,520 1,928 2,032 2,410 2,413 2,540 3,856 4,579 4,820 4,826 5,080 9,158 9,640 9,652 10,160 12,065 18,316 19,280 19,304 22,895 24,130 30,607 36,632 38,608 45,790 48,260 61,214 73,264 91,580 96,520 122,428

Collatz Trajectory (217 steps to reach 1)

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

46,522,640 23,261,320 11,630,660 5,815,330 2,907,665 8,722,996 4,361,498 2,180,749 6,542,248 3,271,124 1,635,562 817,781 2,453,344 1,226,672 613,336 306,668 153,334 76,667 230,002 115,001 345,004 172,502 86,251 258,754 129,377 388,132 194,066 97,033 291,100 145,550 72,775 218,326 109,163 327,490 163,745 491,236 245,618 122,809 368,428 184,214 92,107 276,322 138,161 414,484 207,242 103,621 310,864 155,432 77,716 38,858 19,429 58,288 29,144 14,572 7,286 3,643 10,930 5,465 16,396 8,198

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