λ
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Atlas › Integer Profiles › Node 78,803,648

78,803,648

26 × 7 × 11 × 15991
Abundant Even Composite

78,803,648 factors as 2^6 × 7 × 11 × 15991. Its 56 positive divisors give a proper-divisor sum of 116,170,816, so this integer is abundant. The Collatz stopping time is 179 steps.

Prime Factor Structure

Factorization String 2^6 × 7 × 11 × 15991
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 194,974,464
Proper Divisor Sum 116,170,816
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #78803639 ← → #78803651

Radix Representation

Decimal 78803648
Binary 100101100100111001011000000 (27 bits)
Octal 0o454471300
Hexadecimal 0x4B272C0

Divisor Catalog (56)

1 2 4 7 8 11 14 16 22 28 32 44 56 64 77 88 112 154 176 224 308 352 448 616 704 1,232 2,464 4,928 15,991 31,982 63,964 111,937 127,928 175,901 223,874 255,856 351,802 447,748 511,712 703,604 895,496 1,023,424 1,231,307 1,407,208 1,790,992 2,462,614 2,814,416 3,581,984 4,925,228 5,628,832 7,163,968 9,850,456 11,257,664 19,700,912 39,401,824 78,803,648

Collatz Trajectory (179 steps to reach 1)

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

78,803,648 39,401,824 19,700,912 9,850,456 4,925,228 2,462,614 1,231,307 3,693,922 1,846,961 5,540,884 2,770,442 1,385,221 4,155,664 2,077,832 1,038,916 519,458 259,729 779,188 389,594 194,797 584,392 292,196 146,098 73,049 219,148 109,574 54,787 164,362 82,181 246,544 123,272 61,636 30,818 15,409 46,228 23,114 11,557 34,672 17,336 8,668 4,334 2,167 6,502 3,251 9,754 4,877 14,632 7,316 3,658 1,829 5,488 2,744 1,372 686 343 1,030 515 1,546 773 2,320

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