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Atlas › Integer Profiles › Node 7,553,406

7,553,406

2 × 3 × 7 × 17 × 71 × 149
Abundant Even Composite

7,553,406 factors as 2 × 3 × 7 × 17 × 71 × 149. Its 64 positive divisors give a proper-divisor sum of 11,108,994, so this integer is abundant. The Collatz stopping time is 111 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 17 × 71 × 149
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 18,662,400
Proper Divisor Sum 11,108,994
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #7553387 ← → #7553411

Radix Representation

Decimal 7553406
Binary 11100110100000101111110 (23 bits)
Octal 0o34640576
Hexadecimal 0x73417E

Divisor Catalog (60 of 64)

1 2 3 6 7 14 17 21 34 42 51 71 102 119 142 149 213 238 298 357 426 447 497 714 894 994 1,043 1,207 1,491 2,086 2,414 2,533 2,982 3,129 3,621 5,066 6,258 7,242 7,599 8,449 10,579 15,198 16,898 17,731 21,158 25,347 31,737 35,462 50,694 53,193 63,474 74,053 106,386 148,106 179,843 222,159 359,686 444,318 539,529 1,079,058

Collatz Trajectory (111 steps to reach 1)

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

7,553,406 3,776,703 11,330,110 5,665,055 16,995,166 8,497,583 25,492,750 12,746,375 38,239,126 19,119,563 57,358,690 28,679,345 86,038,036 43,019,018 21,509,509 64,528,528 32,264,264 16,132,132 8,066,066 4,033,033 12,099,100 6,049,550 3,024,775 9,074,326 4,537,163 13,611,490 6,805,745 20,417,236 10,208,618 5,104,309 15,312,928 7,656,464 3,828,232 1,914,116 957,058 478,529 1,435,588 717,794 358,897 1,076,692 538,346 269,173 807,520 403,760 201,880 100,940 50,470 25,235 75,706 37,853 113,560 56,780 28,390 14,195 42,586 21,293 63,880 31,940 15,970 7,985

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