λ
Harmonic Matrix

3,515,995

5 × 72 × 113 × 127
Deficient Odd Composite

3,515,995 has digital root 1. The neighboring primes are 3515977 and 3516001; its proper-divisor sum differs from the starting integer by -2,041,526.

Prime Factor Structure

Factorization String 5 × 7^2 × 113 × 127
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 4,990,464
Proper Divisor Sum 1,474,469
Digit Sum / Digital Root 37 (Root: 1)
Adjacent Primes #3515977 ← → #3516001

Radix Representation

Decimal 3515995
Binary 1101011010011001011011 (22 bits)
Octal 0o15323133
Hexadecimal 0x35A65B

Divisor Catalog (24)

1 5 7 35 49 113 127 245 565 635 791 889 3,955 4,445 5,537 6,223 14,351 27,685 31,115 71,755 100,457 502,285 703,199 3,515,995

Collatz Trajectory (146 steps to reach 1)

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

3,515,995 10,547,986 5,273,993 15,821,980 7,910,990 3,955,495 11,866,486 5,933,243 17,799,730 8,899,865 26,699,596 13,349,798 6,674,899 20,024,698 10,012,349 30,037,048 15,018,524 7,509,262 3,754,631 11,263,894 5,631,947 16,895,842 8,447,921 25,343,764 12,671,882 6,335,941 19,007,824 9,503,912 4,751,956 2,375,978 1,187,989 3,563,968 1,781,984 890,992 445,496 222,748 111,374 55,687 167,062 83,531 250,594 125,297 375,892 187,946 93,973 281,920 140,960 70,480 35,240 17,620 8,810 4,405 13,216 6,608 3,304 1,652 826 413 1,240 620

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