A124372 a(n) is the number of earlier terms a(k) such that a(k)*n is of the form m^j, m = integer >= 0, j = integer >= 2.

0, 1, 1, 3, 1, 1, 1, 6, 7, 1, 1, 2, 1, 1, 1, 12, 1, 3, 1, 1, 1, 1, 1, 2, 17, 1, 21, 2, 1, 1, 1, 24, 1, 1, 1, 25, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 37, 5, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 53, 1, 1, 1, 2, 1, 1, 1, 10, 1, 1, 4, 1, 1, 1, 1, 2, 63, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 10, 1, 77

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

12*a(1) = 0 and 12*a(4) = 36 are the two integers of the form m^j (m=nonnegative integer, j = integer >= 2) made by multiplying earlier terms with 12. So a(12) = 2.

Mathematica

f[l_List] := Append[l, Length[Select[(Length[l] + 1)*l, # == 0 || GCD @@ Last /@ FactorInteger[ # ] > 1 &]]]; Nest[f, {}, 100] (* Ray Chandler, Oct 29 2006 *)

Prog

(PARI)
up_to = 1001;
prepare_A124372(up_to) = { my(v = vector(up_to), c); v[1] = 0; v[2] = 1; for(n=3, up_to, c=1; for(k=2, n-1, c += (0<ispower(v[k]*n))); v[n] = c); (v); };
v124372 = prepare_A124372(up_to);
A124372(n) = v124372[n]; \\ Antti Karttunen, Jul 21 2018

Crossrefs

Cf. A124371.

Sequence in context: A297672 A256973 A058057 * A126470 A179701 A276996

Adjacent sequences: A124369 A124370 A124371 * A124373 A124374 A124375

Keyword

easy,nonn

Author

Leroy Quet, Oct 27 2006

Extensions

Extended by Ray Chandler, Oct 29 2006

Status

approved