A286535 - OEIS

%I #6 May 17 2017 17:56:20

%S 1,2,2,3,2,3,4,5,2,3,4,5,4,6,6,7,2,3,4,5,4,6,6,7,4,6,8,9,6,10,9,11,2,

%T 3,4,5,4,6,6,7,4,6,8,9,6,10,9,11,4,6,8,9,8,12,12,13,6,10,12,14,9,14,

%U 13,15,2,3,4,5,4,6,6,7,4,6,8,9,6,10,9,11,4,6,8,9,8,12,12,13,6,10,12,14,9,14,13,15,4,6,8,9,8,12,12,13,8,12,16,17,12,18

%N Restricted growth sequence of A278535 (prime-signature of A253565).

%H Antti Karttunen, <a href="/A286535/b286535.txt">Table of n, a(n) for n = 0..65537</a>

%o (PARI)

%o rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };

%o write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After _M. F. Hasler_'s code for A006530.

%o A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));

%o A253560(n) = if(1==n, 1, (n*prime(A061395(n))));

%o A253565(n) = if(n<2,(1+n),if(!(n%2),A253550(A253565(n/2)),A253560(A253565((n-1)/2)))); \\ Would be better if memoized!

%o A278535(n) = A046523(A253565(n));

%o write_to_bfile(0,rgs_transform(vector(65538,n,A278535(n-1))),"b286535.txt");

%Y Cf. A046523, A253565, A286531, A286533, A286622.

%K nonn

%O 0,2

%A _Antti Karttunen_, May 17 2017