7,834,736

2⁴ × 7 × 13 × 5381

Starting at 7,834,736, the Collatz iteration reaches 1 after 155 steps. The first transition is 3917368; the starting value is even with 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 7 × 13 × 5381

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 18,686,304

Proper Divisor Sum 10,851,568

Digit Sum / Digital Root 38 (Root: 2)

Adjacent Primes #7834721 ← → #7834747

Radix Representation

Decimal	7834736
Binary	11101111000110001110000 (23 bits)
Octal	0o35706160
Hexadecimal	0x778C70

Divisor Catalog (40)

1 2 4 7 8 13 14 16 26 28 52 56 91 104 112 182 208 364 728 1,456 5,381 10,762 21,524 37,667 43,048 69,953 75,334 86,096 139,906 150,668 279,812 301,336 489,671 559,624 602,672 979,342 1,119,248 1,958,684 3,917,368 7,834,736

Collatz Trajectory (155 steps to reach 1)

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

7,834,736 3,917,368 1,958,684 979,342 489,671 1,469,014 734,507 2,203,522 1,101,761 3,305,284 1,652,642 826,321 2,478,964 1,239,482 619,741 1,859,224 929,612 464,806 232,403 697,210 348,605 1,045,816 522,908 261,454 130,727 392,182 196,091 588,274 294,137 882,412 441,206 220,603 661,810 330,905 992,716 496,358 248,179 744,538 372,269 1,116,808 558,404 279,202 139,601 418,804 209,402 104,701 314,104 157,052 78,526 39,263 117,790 58,895 176,686 88,343 265,030 132,515 397,546 198,773 596,320 298,160

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