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Atlas › Integer Profiles › Node 7,798,536

7,798,536

23 × 32 × 89 × 1217
Abundant Even Composite

7,798,536 factors as 2^3 × 3^2 × 89 × 1217. Its 48 positive divisors give a proper-divisor sum of 13,577,364, so this integer is abundant. The Collatz stopping time is 217 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 89 × 1217
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 21,375,900
Proper Divisor Sum 13,577,364
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #7798501 ← → #7798537

Radix Representation

Decimal 7798536
Binary 11101101111111100001000 (23 bits)
Octal 0o35577410
Hexadecimal 0x76FF08

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 72 89 178 267 356 534 712 801 1,068 1,217 1,602 2,136 2,434 3,204 3,651 4,868 6,408 7,302 9,736 10,953 14,604 21,906 29,208 43,812 87,624 108,313 216,626 324,939 433,252 649,878 866,504 974,817 1,299,756 1,949,634 2,599,512 3,899,268 7,798,536

Collatz Trajectory (217 steps to reach 1)

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

7,798,536 3,899,268 1,949,634 974,817 2,924,452 1,462,226 731,113 2,193,340 1,096,670 548,335 1,645,006 822,503 2,467,510 1,233,755 3,701,266 1,850,633 5,551,900 2,775,950 1,387,975 4,163,926 2,081,963 6,245,890 3,122,945 9,368,836 4,684,418 2,342,209 7,026,628 3,513,314 1,756,657 5,269,972 2,634,986 1,317,493 3,952,480 1,976,240 988,120 494,060 247,030 123,515 370,546 185,273 555,820 277,910 138,955 416,866 208,433 625,300 312,650 156,325 468,976 234,488 117,244 58,622 29,311 87,934 43,967 131,902 65,951 197,854 98,927 296,782

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