A336429 First location of n in A331025 or 0 if number is absent.

1, 0, 2, 3, 5, 7, 11, 13, 4, 17, 19, 6, 23, 29, 10, 9, 31, 14, 37, 15, 22, 41, 43, 21, 25, 47, 8, 33, 53, 34, 59, 39, 38, 61, 55, 12, 67, 71, 46, 51, 73, 58, 79, 57, 20, 83, 89, 18, 121, 85, 62, 69, 97, 28, 95, 87, 74, 101, 103, 30, 107, 109, 44, 27, 115, 82

Offset

1,3

Comments

26 is the smallest number not in this sequence; A331025(21) and A331025(26) both equal 24; the smallest number to occur in A331025 at least twice.

Links

Table of n, a(n) for n=1..66.

Example

a(9) = 4 because A331025(4) = 9 and no earlier term of A331025 is 9.

Mathematica

Block[{nn = 66, s}, s = Select[Range[3 nn], And[# != 2, Or[Log2[#] == 3, PrimeQ@ #, PrimeQ[#/2]]] &]; Insert[#, 0, 2][[1 ;; nn]] &@ Values[KeySort@ PositionIndex@ Array[Times @@ Map[If[#[[1]] == 1, 1, # /. {p_, e_} :> s[[PrimePi@ p]]^e] &, FactorInteger[#]] &, Prime@ Length@ s]][[All, 1]]] (* Michael De Vlieger, Aug 21 2020 *)

Prog

(PARI) isp(n) = (isprime(n) && (n%2)) || (n==8) || (!(n%2) && isprime(n/2)); \\ A232803
vA331025(nn) = {my(vall = [1..nn]); my(vp = select(x->isp(x), vall)); for (n=2, nn, my(f=factor(n)); for (k=1, #f~, f[k, 1] = vp[primepi(f[k, 1])]); vall[n] = factorback(f); ); vall; }
lista(nn) = {my(vall = vA331025(nn)); my(vr = vector(nn)); for (n=1, nn, my(vs = select(x->(x==n), vall, 1)); if (#vs == 0, vr[n] = 0, vr[n] = vs[1]); ); my(vz = select(x->(x==0), vr, 1)); if (#vz > 1, vr = vector(vz[2]-1, k, vr[k]); ); vr; } \\ Michel Marcus, Sep 14 2020

Crossrefs

Cf. A232803, A331025.

Sequence in context: A142713 A039712 A072700 * A072698 A034442 A077620

Adjacent sequences: A336426 A336427 A336428 * A336430 A336431 A336432

Keyword

nonn

Author

J. Lowell, Jul 21 2020

Extensions

More terms from Rémy Sigrist, Jul 21 2020

Status

approved