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Atlas › Integer Profiles › Node 7,772,076

7,772,076

22 × 32 × 13 × 16607
Abundant Even Composite

7,772,076 factors as 2^2 × 3^2 × 13 × 16607. Its 36 positive divisors give a proper-divisor sum of 13,386,516, so this integer is abundant. The Collatz stopping time is 279 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 13 × 16607
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 21,158,592
Proper Divisor Sum 13,386,516
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #7772059 ← → #7772101

Radix Representation

Decimal 7772076
Binary 11101101001011110101100 (23 bits)
Octal 0o35513654
Hexadecimal 0x7697AC

Divisor Catalog (36)

1 2 3 4 6 9 12 13 18 26 36 39 52 78 117 156 234 468 16,607 33,214 49,821 66,428 99,642 149,463 199,284 215,891 298,926 431,782 597,852 647,673 863,564 1,295,346 1,943,019 2,590,692 3,886,038 7,772,076

Collatz Trajectory (279 steps to reach 1)

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

7,772,076 3,886,038 1,943,019 5,829,058 2,914,529 8,743,588 4,371,794 2,185,897 6,557,692 3,278,846 1,639,423 4,918,270 2,459,135 7,377,406 3,688,703 11,066,110 5,533,055 16,599,166 8,299,583 24,898,750 12,449,375 37,348,126 18,674,063 56,022,190 28,011,095 84,033,286 42,016,643 126,049,930 63,024,965 189,074,896 94,537,448 47,268,724 23,634,362 11,817,181 35,451,544 17,725,772 8,862,886 4,431,443 13,294,330 6,647,165 19,941,496 9,970,748 4,985,374 2,492,687 7,478,062 3,739,031 11,217,094 5,608,547 16,825,642 8,412,821 25,238,464 12,619,232 6,309,616 3,154,808 1,577,404 788,702 394,351 1,183,054 591,527 1,774,582

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