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Atlas › Integer Profiles › Node 77,382,592

77,382,592

26 × 7 × 19 × 9091
Abundant Even Composite

77,382,592 factors as 2^6 × 7 × 19 × 9091. Its 56 positive divisors give a proper-divisor sum of 107,366,848, so this integer is abundant. The Collatz stopping time is 73 steps.

Prime Factor Structure

Factorization String 2^6 × 7 × 19 × 9091
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 184,749,440
Proper Divisor Sum 107,366,848
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #77382559 ← → #77382619

Radix Representation

Decimal 77382592
Binary 100100111001100001111000000 (27 bits)
Octal 0o447141700
Hexadecimal 0x49CC3C0

Divisor Catalog (56)

1 2 4 7 8 14 16 19 28 32 38 56 64 76 112 133 152 224 266 304 448 532 608 1,064 1,216 2,128 4,256 8,512 9,091 18,182 36,364 63,637 72,728 127,274 145,456 172,729 254,548 290,912 345,458 509,096 581,824 690,916 1,018,192 1,209,103 1,381,832 2,036,384 2,418,206 2,763,664 4,072,768 4,836,412 5,527,328 9,672,824 11,054,656 19,345,648 38,691,296 77,382,592

Collatz Trajectory (73 steps to reach 1)

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

77,382,592 38,691,296 19,345,648 9,672,824 4,836,412 2,418,206 1,209,103 3,627,310 1,813,655 5,440,966 2,720,483 8,161,450 4,080,725 12,242,176 6,121,088 3,060,544 1,530,272 765,136 382,568 191,284 95,642 47,821 143,464 71,732 35,866 17,933 53,800 26,900 13,450 6,725 20,176 10,088 5,044 2,522 1,261 3,784 1,892 946 473 1,420 710 355 1,066 533 1,600 800 400 200 100 50 25 76 38 19 58 29 88 44 22 11

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