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Atlas › Integer Profiles › Node 34,926,640

34,926,640

24 × 5 × 7 × 47 × 1327
Abundant Even Composite

34,926,640 factors as 2^4 × 5 × 7 × 47 × 1327. Its 80 positive divisors give a proper-divisor sum of 59,924,432, so this integer is abundant. The Collatz stopping time is 214 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 47 × 1327
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 94,851,072
Proper Divisor Sum 59,924,432
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #34926637 ← → #34926641

Radix Representation

Decimal 34926640
Binary 10000101001111000000110000 (26 bits)
Octal 0o205170060
Hexadecimal 0x214F030

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 28 35 40 47 56 70 80 94 112 140 188 235 280 329 376 470 560 658 752 940 1,316 1,327 1,645 1,880 2,632 2,654 3,290 3,760 5,264 5,308 6,580 6,635 9,289 10,616 13,160 13,270 18,578 21,232 26,320 26,540 37,156 46,445 53,080 62,369 74,312 92,890 106,160 124,738 148,624 185,780

Collatz Trajectory (214 steps to reach 1)

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

34,926,640 17,463,320 8,731,660 4,365,830 2,182,915 6,548,746 3,274,373 9,823,120 4,911,560 2,455,780 1,227,890 613,945 1,841,836 920,918 460,459 1,381,378 690,689 2,072,068 1,036,034 518,017 1,554,052 777,026 388,513 1,165,540 582,770 291,385 874,156 437,078 218,539 655,618 327,809 983,428 491,714 245,857 737,572 368,786 184,393 553,180 276,590 138,295 414,886 207,443 622,330 311,165 933,496 466,748 233,374 116,687 350,062 175,031 525,094 262,547 787,642 393,821 1,181,464 590,732 295,366 147,683 443,050 221,525

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