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Atlas › Integer Profiles › Node 78,464,952

78,464,952

23 × 32 × 29 × 37579
Abundant Even Composite

78,464,952 factors as 2^3 × 3^2 × 29 × 37579. Its 48 positive divisors give a proper-divisor sum of 141,378,048, so this integer is abundant. The Collatz stopping time is 166 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 29 × 37579
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 219,843,000
Proper Divisor Sum 141,378,048
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #78464951 ← → #78464957

Radix Representation

Decimal 78464952
Binary 100101011010100011110111000 (27 bits)
Octal 0o453243670
Hexadecimal 0x4AD47B8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 29 36 58 72 87 116 174 232 261 348 522 696 1,044 2,088 37,579 75,158 112,737 150,316 225,474 300,632 338,211 450,948 676,422 901,896 1,089,791 1,352,844 2,179,582 2,705,688 3,269,373 4,359,164 6,538,746 8,718,328 9,808,119 13,077,492 19,616,238 26,154,984 39,232,476 78,464,952

Collatz Trajectory (166 steps to reach 1)

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

78,464,952 39,232,476 19,616,238 9,808,119 29,424,358 14,712,179 44,136,538 22,068,269 66,204,808 33,102,404 16,551,202 8,275,601 24,826,804 12,413,402 6,206,701 18,620,104 9,310,052 4,655,026 2,327,513 6,982,540 3,491,270 1,745,635 5,236,906 2,618,453 7,855,360 3,927,680 1,963,840 981,920 490,960 245,480 122,740 61,370 30,685 92,056 46,028 23,014 11,507 34,522 17,261 51,784 25,892 12,946 6,473 19,420 9,710 4,855 14,566 7,283 21,850 10,925 32,776 16,388 8,194 4,097 12,292 6,146 3,073 9,220 4,610 2,305

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