A318831 - OEIS

%I #8 Sep 05 2018 06:12:25

%S 1,1,1,1,1,1,2,1,2,1,3,1,2,2,1,1,1,2,3,1,2,3,4,1,3,2,3,2,5,1,6,1,3,1,

%T 2,2,3,3,2,1,3,2,7,3,2,4,8,1,7,3,1,2,4,3,3,2,3,5,8,1,6,6,3,1,2,3,3,1,

%U 4,2,4,2,3,3,3,3,6,2,8,1,9,3,7,2,1,7,5,3,4,2,3,4,6,8,3,1,2,7,6,3,4,1,9,2,2

%N Restricted growth sequence transform of A278222(A000010(n)).

%C Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary expansion of A000010(n).

%C For all i, j: a(i) = a(j) => A295660(i) = A295660(j).

%H Antti Karttunen, <a href="/A318831/b318831.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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; };

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

%o A278222(n) = A046523(A005940(1+n));

%o v318831 = rgs_transform(vector(up_to,n,A278222(eulerphi(n))));

%o A318831(n) = v318831[n];

%Y Cf. also A000010, A278222, A295660, A318835.

%Y Compare also with the scatterplots of A286622, A304101 and A318832.

%K nonn

%O 1,7

%A _Antti Karttunen_, Sep 04 2018