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URL: https://oeis.org/A124372

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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.
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
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
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Oct 27 2006
EXTENSIONS
Extended by Ray Chandler, Oct 29 2006
STATUS
approved