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URL: https://oeis.org/A333235

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A333235
a(n) is the product of indices of unitary prime power divisors of n.
3
1, 1, 2, 3, 4, 2, 5, 6, 7, 4, 8, 6, 9, 5, 8, 10, 11, 7, 12, 12, 10, 8, 13, 12, 14, 9, 15, 15, 16, 8, 17, 18, 16, 11, 20, 21, 19, 12, 18, 24, 20, 10, 21, 24, 28, 13, 22, 20, 23, 14, 22, 27, 24, 15, 32, 30, 24, 16, 25, 24, 26, 17, 35, 27, 36, 16, 28, 33, 26, 20
OFFSET
1,3
COMMENTS
Equivalently: replace each prime power p^e in the prime factorization of n by its index in A246655. - M. F. Hasler, Jun 16 2021
LINKS
FORMULA
If n = Product (p_j^k_j) then a(n) = Product (A025528(p_j^k_j)).
a(prime(n)) = A027883(n).
a(2^n) = A182908(n).
a(A246655(n)) = n.
EXAMPLE
a(600) = a(2^3 * 3 * 5^2) = a(A246655(6) * A246655(2) * A246655(14)) = 6 * 2 * 14 = 168.
MAPLE
N:= 1000: # for a(1)..a(N)
R:= NULL: p:= 2:
while p < N do
R:= R, seq(p^k, k=1..ilog[p](N));
p:= nextprime(p);
od:
L:= sort([R]):
f:= proc(n) local F, t;
F:= ifactors(n)[2];
mul(ListTools:-BinarySearch(L, t[1]^t[2]), t=F)
end proc:
map(f, [$1..N]); # Robert Israel, Feb 11 2021
MATHEMATICA
PrimePowerPi[n_] := Sum[Boole[PrimePowerQ[k]], {k, 1, n}]; a[1] = 1; a[n_] := Times @@ (PrimePowerPi[#[[1]]^#[[2]]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 70}]
PROG
(PARI) apply( {A333235(n)=vecprod([A322981(f[1]^f[2])|f<-factor(n)~])}, [1..99]) \\ M. F. Hasler, Jun 16 2021
CROSSREFS
Cf. A322981 (the index of n = p^e in A246655).
Sequence in context: A369422 A361020 A368693 * A295887 A387835 A293450
KEYWORD
nonn,mult,look
AUTHOR
Ilya Gutkovskiy, Mar 12 2020
STATUS
approved