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Atlas › Integer Profiles › Node 7,689,006

7,689,006

2 × 35 × 13 × 1217
Abundant Even Composite

7,689,006 factors as 2 × 3^5 × 13 × 1217. Its 48 positive divisors give a proper-divisor sum of 10,931,778, so this integer is abundant. The Collatz stopping time is 173 steps.

Prime Factor Structure

Factorization String 2 × 3^5 × 13 × 1217
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 18,620,784
Proper Divisor Sum 10,931,778
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #7688999 ← → #7689043

Radix Representation

Decimal 7689006
Binary 11101010101001100101110 (23 bits)
Octal 0o35251456
Hexadecimal 0x75532E

Divisor Catalog (48)

1 2 3 6 9 13 18 26 27 39 54 78 81 117 162 234 243 351 486 702 1,053 1,217 2,106 2,434 3,159 3,651 6,318 7,302 10,953 15,821 21,906 31,642 32,859 47,463 65,718 94,926 98,577 142,389 197,154 284,778 295,731 427,167 591,462 854,334 1,281,501 2,563,002 3,844,503 7,689,006

Collatz Trajectory (173 steps to reach 1)

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

7,689,006 3,844,503 11,533,510 5,766,755 17,300,266 8,650,133 25,950,400 12,975,200 6,487,600 3,243,800 1,621,900 810,950 405,475 1,216,426 608,213 1,824,640 912,320 456,160 228,080 114,040 57,020 28,510 14,255 42,766 21,383 64,150 32,075 96,226 48,113 144,340 72,170 36,085 108,256 54,128 27,064 13,532 6,766 3,383 10,150 5,075 15,226 7,613 22,840 11,420 5,710 2,855 8,566 4,283 12,850 6,425 19,276 9,638 4,819 14,458 7,229 21,688 10,844 5,422 2,711 8,134

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