A336925 - OEIS

%I #6 Aug 10 2020 22:19:20

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

%T 19,13,1,3,20,3,21,22,15,17,23,12,24,9,25,26,19,3,2,27,28,19,13,20,29,

%U 19,29,5,23,15,4,11,24,30,1,25,31,32,33,24,31,19,6,9,34,2,35,24,4,5,36,37,33,25,9,38,39,29,40,23,41,42,4,43,31,29,44,13,45,46,47,48,49,30

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A336147(1+sigma(i)) = A336147(1+sigma(j)), for all i, j >= 1.

%C Restricted growth sequence transform of the function f(n) = A336147(A088580(n)).

%C For all i, j:

%C   A324400(i) = A324400(j) => a(i) = a(j),

%C   a(i) = a(j) => A336691(i) = A336691(j),

%C   a(i) = a(j) => A336924(i) = A336924(j).

%H Antti Karttunen, <a href="/A336925/b336925.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</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 A020639(n) = if(1==n, n, factor(n)[1, 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 A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));

%o A278221(n) = A046523(A122111(n));

%o Aux336147(n) = [A020639(n),A278221(n)];

%o v336925 = rgs_transform(vector(up_to, n, Aux336147(1+sigma(n))));

%o A336925(n) = v336925[n];

%Y Cf. also A336926.

%K nonn

%O 1,3

%A _Antti Karttunen_, Aug 10 2020