A300229 Restricted growth sequence transform of A285729, combining A032742(n) and A046523(n), the largest proper divisor and the prime signature of n.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 7, 10, 2, 11, 2, 12, 9, 13, 2, 14, 15, 16, 17, 18, 2, 19, 2, 20, 13, 21, 9, 22, 2, 23, 16, 24, 2, 25, 2, 26, 27, 28, 2, 29, 30, 31, 21, 32, 2, 33, 13, 34, 23, 35, 2, 36, 2, 37, 38, 39, 16, 40, 2, 41, 28, 42, 2, 43, 2, 44, 31, 45, 13, 46, 2, 47, 48, 49, 2, 50, 21, 51, 35, 52, 2, 53, 16, 54, 37, 55, 23, 56, 2, 57

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

a(10) = a(15) (= 7) because both are nonsquare semiprimes (2*5 and 3*5), and when the smallest prime factor is divided out, both yield the same quotient, 5.

Prog

(PARI)
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A285729(n) = (1/2)*(2 + ((A032742(n)+A046523(n))^2) - A032742(n) - 3*A046523(n));
write_to_bfile(1, rgs_transform(vector(65537, n, A285729(n))), "b300229.txt");

Crossrefs

Cf. A032742, A046523, A285729.

Cf. also A300223, A300226, A300230, A300231, A300232, A300233, A300235.

Sequence in context: A326192 A323245 A323240 * A300825 A355000 A300232

Adjacent sequences: A300226 A300227 A300228 * A300230 A300231 A300232

Keyword

nonn

Author

Antti Karttunen, Mar 01 2018

Status

approved