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

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..269

Example

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'.

Prog

(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

Crossrefs

Cf. A003415.

Subsequence of A218011.

Sequence in context: A044380 A044761 A248456 * A346293 A244178 A131683

Adjacent sequences: A370123 A370124 A370125 * A370127 A370128 A370129

Keyword

nonn

Author

Antti Karttunen, Feb 21 2024

Status

approved