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Atlas › Integer Profiles › Node 27,282,968

27,282,968

23 × 23 × 29 × 5113
Abundant Even Composite

27,282,968 factors as 2^3 × 23 × 29 × 5113. Its 32 positive divisors give a proper-divisor sum of 27,948,232, so this integer is abundant. The Collatz stopping time is 136 steps.

Prime Factor Structure

Factorization String 2^3 × 23 × 29 × 5113
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 55,231,200
Proper Divisor Sum 27,948,232
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #27282961 ← → #27282971

Radix Representation

Decimal 27282968
Binary 1101000000100111000011000 (25 bits)
Octal 0o150047030
Hexadecimal 0x1A04E18

Divisor Catalog (32)

1 2 4 8 23 29 46 58 92 116 184 232 667 1,334 2,668 5,113 5,336 10,226 20,452 40,904 117,599 148,277 235,198 296,554 470,396 593,108 940,792 1,186,216 3,410,371 6,820,742 13,641,484 27,282,968

Collatz Trajectory (136 steps to reach 1)

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

27,282,968 13,641,484 6,820,742 3,410,371 10,231,114 5,115,557 15,346,672 7,673,336 3,836,668 1,918,334 959,167 2,877,502 1,438,751 4,316,254 2,158,127 6,474,382 3,237,191 9,711,574 4,855,787 14,567,362 7,283,681 21,851,044 10,925,522 5,462,761 16,388,284 8,194,142 4,097,071 12,291,214 6,145,607 18,436,822 9,218,411 27,655,234 13,827,617 41,482,852 20,741,426 10,370,713 31,112,140 15,556,070 7,778,035 23,334,106 11,667,053 35,001,160 17,500,580 8,750,290 4,375,145 13,125,436 6,562,718 3,281,359 9,844,078 4,922,039 14,766,118 7,383,059 22,149,178 11,074,589 33,223,768 16,611,884 8,305,942 4,152,971 12,458,914 6,229,457

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