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

Author

Antti Karttunen, Mar 01 2018

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A032742, A046523, A285729.

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

Programs

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");