A295300 - OEIS

%I #18 Jul 13 2019 09:11:54

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,17,18,19,20,21,22,23,24,25,

%T 26,27,28,29,30,31,32,33,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,

%U 48,44,49,50,51,44,52,53,54,55,56,57,58,59,60,61,62,63,64,58,62,65,66,67,68,69,70,58,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,80

%N Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003557(n), A046523(n), A048250(n)].

%C Restricted growth sequence transform of A291752.

%C For all i, j:

%C   a(i) = a(j) => A291751(i) = A291751(j),

%C   a(i) = a(j) => A326199(i) = A326199(j) => A294877(i) = A294877(j),

%C   a(i) = a(j) => A322021(i) = A322021(j),

%C   a(i) = a(j) => A295888(i) = A295888(j),

%C   a(i) = a(j) => A296090(i) = A296090(j).

%H Antti Karttunen, <a href="/A295300/b295300.txt">Table of n, a(n) for n = 1..100000</a>

%o (PARI)

%o up_to = 100000;

%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 A003557(n) = n/factorback(factor(n)[, 1]); \\ From A003557

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

%o A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));

%o A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));

%o Aux295300(n) = (1/2)*(2 + ((A046523(n) + A291750(n))^2) - A046523(n) - 3*A291750(n));

%o v295300 = rgs_transform(vector(up_to,n,Aux295300(n)));

%o A295300(n) = v295300[n];

%Y Cf. A003557, A046523, A048250, A101296, A286360, A291750, A291751, A291752, A291757, A291758, A295888, A296090, A322021, A326199.

%Y Cf. also A305801, A305900, A323368, A324400.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 19 2017

%E Name changed and the comments section added by _Antti Karttunen_, Jul 13 2019