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

Author

Antti Karttunen, Feb 21 2024

Keywords

• nonn

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

Crossrefs

Cf. A003415.

Subsequence of A218011.

Programs

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