A264762 a(n) is the index of A246946(n) in A024619, integers x that satisfy omega(x) >= 2.

1, 3, 6, 10, 13, 2, 7, 20, 26, 34, 5, 23, 44, 55, 17, 21, 4, 12, 31, 41, 16, 67, 8, 36, 50, 25, 29, 38, 9, 22, 54, 70, 30, 113, 14, 63, 86, 42, 47, 11, 28, 66, 85, 37, 136, 19, 76, 106, 61, 65, 15, 39, 90, 116, 48, 64, 79, 69, 73, 18, 45, 102, 133, 60, 207, 32, 117, 164

Offset

1,2

Comments

Is this a permutation of the positive integers?

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The first 6 terms of A246946 are 6, 12, 18, 24, 30 and 10, that is, the 1st, 3rd, 6th, 10th, 13th and 2nd terms of A024619.

Maple

N:= 2000: # get all terms before the first term > N.
W:= Vector(N, t -> if nops(numtheory:-factorset(t))<=1 then 0 else 1 fi):
WS:= ListTools:-PartialSums(convert(W, list)):
m:= 1:
F:= {2, 3}:
A[1]:= WS[6]:
W[6]:= 0:
for n from 2 do
  while W[m] = 0 and m < N do m:= m+1 od;
  for k from m to N do
     if W[k] = 1 and nops(numtheory:-factorset(k) intersect F) = 2 then
        A[n]:= WS[k];
        W[k]:= 0;
        F:= numtheory:-factorset(k);
        break
     fi
  od;
  if k > N then break fi;
od:
seq(A[i], i=1..n-1); # Robert Israel, Nov 23 2015

Prog

(PARI) v246946(nn) = {a = 6; fa = (factor(a)[, 1])~; va = [a]; vs = va; k = 0; while (k!= nn, k = 1; while (!((#setintersect(fa, (factor(k)[, 1])~) == 2) && (! vecsearch(vs, k))), k++); a = k; fa = (factor(a)[, 1])~; va = concat(va, k); vs = vecsort(va); ); va; }
v024619(nn) = {va = []; for (n=1, nn, if (omega(n) >= 2, va = concat(va, n)); ); va; }
lista(nn) = {v = v246946(nn); w = v024619(vecmax(v)); for (k=1, #v, for (j=1, #w, if (w[j] == v[k], print1(j, ", "); break); ); ); }

Crossrefs

Cf. A024619, A246946.

Sequence in context: A131696 A164114 A167219 * A028357 A310047 A310048

Adjacent sequences: A264759 A264760 A264761 * A264763 A264764 A264765

Keyword

nonn

Author

Michel Marcus, Nov 23 2015

Status

approved