A264780 - OEIS

%I #9 Nov 26 2015 03:39:54

%S 1,3,8,13,19,26,33,2,7,14,23,43,57,67,81,93,5,18,52,72,115,138,164,10,

%T 63,127,200,240,41,49,58,66,4,16,31,47,85,107,20,60,159,214,11,34,100,

%U 134,175,22,118,234,296,75,84,6,21,39,62,109,133,27,76,197,265

%N a(n) is the index of A246947(n) in A000977.

%C Is this a permutation of the positive integers?

%H Robert Israel, <a href="/A264780/b264780.txt">Table of n, a(n) for n = 1..10000</a>

%e The first 5 terms of A246947 are 30, 60, 90, 120, and 150, that is, the 1st, 3rd, 8th, 13th and 19th terms of A000977.

%p N:= 1000: # get all terms before the first term > N

%p W:= Vector(N, t -> if nops(numtheory:-factorset(t))<=2 then 0 else 1 fi):

%p WS:= ListTools:-PartialSums(convert(W, list)):

%p m:= 1:

%p F:= {2, 3,5}:

%p A[1]:= WS[30]:

%p W[30]:= 0:

%p for n from 2 do

%p     while W[m] = 0 and m < N do m:= m+1 od;

%p   for k from m to N do

%p      if W[k] = 1 and nops(numtheory:-factorset(k) intersect F) = 3 then

%p         A[n]:= WS[k];

%p         W[k]:= 0;

%p         F:= numtheory:-factorset(k);

%p         break

%p      fi

%p   od;

%p   if k > N then break fi;

%p od:

%p seq(A[i],i=1..n-1); # _Robert Israel_, Nov 26 2015

%o (PARI) v246947(nn) = {a = 30; fa = (factor(a)[,1])~; va = [a]; vs = va; k = 0; while (k < nn, k = 1; while (!((#setintersect(fa, (factor(k)[,1])~) == 3) && (! vecsearch(vs, k))), k++); a = k; fa = (factor(a)[,1])~; va = concat(va, k); vs = vecsort(va);); va;}

%o v000977(nn) = {va = []; for (n=1, nn, if (omega(n) >= 3, va = concat(va, n));); va;}

%o lista(nn) = {v = v246947(nn); w = v000977(vecmax(v)); for (k=1, #v, for (j=1, #w, if (w[j] == v[k], print1(j, ", "); break);););}

%Y Cf. A000977, A246947, A264762.

%K nonn

%O 1,2

%A _Michel Marcus_, Nov 24 2015