A351260 - OEIS

%I #8 Feb 06 2022 23:03:11

%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,

%T 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,

%U 28,40,41,42,2,43,2,44,45,46,47,48,2,49,50,51,2,52,2,53,54,55,47,56,2,57,58,59,2,60,41,61,62,63,2,64,37,65,66,67,68,69,2,70,71,72,2,73,2,74,56

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A046523(i) = A046523(j), for all i, j >= 1.

%C Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A046523(n)].

%C For all i, j >= 1:

%C   A305800(i) = A305800(j) => a(i) = a(j),

%C   a(i) = a(j) => A294877(i) = A294877(j),

%C   a(i) = a(j) => A300249(i) = A300249(j),

%C   a(i) = a(j) => A344025(i) = A344025(j).

%H Antti Karttunen, <a href="/A351260/b351260.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 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

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

%o Aux351260(n) = [A003415(n), A003557(n), A046523(n)];

%o v351260 = rgs_transform(vector(up_to,n,Aux351260(n)));

%o A351260(n) = v351260[n];

%Y Cf. A003415, A003557, A046523.

%Y Cf. also A305800, A294877, A300249, A344025.

%Y Differs from A300235, A305895 and A327931 for the first time at n=105, where a(105) = 56, while A300235(105) = A305895(105) = A327931(105) = 75.

%Y Differs from A300249 for the first time at n=425, where a(425) = 299, while A300249(425) = 198.

%K nonn,easy

%O 1,2

%A _Antti Karttunen_, Feb 06 2022