A370126 Numbers k for which k’ = x’*y’, where k = x + y with x and y composite, and k’, x’, y’ are the arithmetic derivatives of k, x, y.
48, 160, 208, 212, 236, 252, 268, 496, 612, 752, 1040, 1172, 1376, 1476, 1568, 1584, 1692, 1728, 2016, 2192, 2736, 3616, 3627, 3632, 3760, 3932, 4048, 4508, 4572, 5264, 5392, 5900, 6224, 6336, 6640, 6652, 6948, 7376, 7648, 8244, 8928, 9072, 9392, 9712, 10648, 10736, 10960, 12500, 12544, 12592, 12960, 13284, 16452
Offset: 1
Keywords
Examples
48 is included as 48 = 15+33, and 15' * 33' = 8*14 = 112 = 48' = A003415(48). 1728 (= 2^6 * 3^3) is included as 1728 = 4+1724, and 4' * 1724' = 4*1728 = 6912 = 1728'. 3627 is included as 3627 = 38+3589, and 38' * 3589' = 21*134 = 2814 = 3627'.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..269
Programs
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PARI
up_to = 2^18; A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1])); v003415 = vector(up_to,n,A003415(n)); isA370126(n) = { my(z=v003415[n]); for(x=2,ceil(n/2),if(!isprime(x) && !isprime(n-x) && !(z%v003415[x]), if(z==v003415[x]*v003415[n-x], return(1)))); (0); }; \\ Antti Karttunen, Feb 22 2024