

A284018


The smallest square referenced in A038109 (Divisible exactly by the square of a prime).


3



4, 9, 4, 9, 4, 25, 4, 4, 4, 9, 49, 25, 4, 4, 9, 4, 9, 25, 4, 4, 9, 4, 49, 9, 4, 4, 4, 9, 121, 4, 9, 4, 4, 9, 49, 4, 25, 9, 4, 4, 169, 9, 4, 25, 4, 4, 4, 9, 25, 4, 9, 4, 4, 9, 4, 9, 4, 121, 4, 49, 4, 4, 9, 4, 25, 4, 9, 4, 9, 289, 4, 49, 4, 9, 4, 9, 4, 4, 25, 4
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OFFSET

1,1


COMMENTS

a(n) = p^2 where p is the least prime whose exponent in the prime factorization of A038109(n) is exactly 2.  Robert Israel, Mar 28 2017


LINKS

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


EXAMPLE

A038109(3)=12, 12 = 2*2*3, so 12 is divisible by the square of 2 which is 4.


MAPLE

N:= 1000: # to use the members of A038109 <= N
P:= select(isprime, [$1..floor(sqrt(N))]):
S:= {}:
for p in P do
Ks:= select(t > t mod p <> 0, {$1..floor(N/p^2)});
R:= map(`*`, Ks, p^2) minus S;
for r in R do B[r]:= p^2 od:
S:= S union R;
od:
A038109:= sort(convert(S, list)): seq(B[A038109[i]], i=1..nops(A038109)); # Robert Israel, Mar 28 2017


CROSSREFS

Cf. A038109, A284017, A013929, A283919.
Sequence in context: A141653 A071793 A010714 * A089090 A204919 A113484
Adjacent sequences: A284015 A284016 A284017 * A284019 A284020 A284021


KEYWORD

nonn


AUTHOR

Robert Price, Mar 18 2017


EXTENSIONS

Corrected by Robert Israel, Mar 28 2017


STATUS

approved



