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A372330
The number of divisors of the smallest multiple of n whose number of divisors is a power of 2 (A036537).
1
1, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 8, 2, 4, 4, 8, 2, 8, 2, 8, 4, 4, 2, 8, 4, 4, 4, 8, 2, 8, 2, 8, 4, 4, 4, 16, 2, 4, 4, 8, 2, 8, 2, 8, 8, 4, 2, 16, 4, 8, 4, 8, 2, 8, 4, 8, 4, 4, 2, 16, 2, 4, 8, 8, 4, 8, 2, 8, 4, 8, 2, 16, 2, 4, 8, 8, 4, 8, 2, 16, 8, 4, 2, 16, 4
OFFSET
1,2
COMMENTS
Also, the number of infinitary divisors of the smallest multiple of n whose number of divisors is a power of 2.
LINKS
FORMULA
a(n) = A000005(A372329(n)).
a(n) = A037445(A372329(n)).
Multiplicative with a(p^e) = 2^ceiling(log_2(e+1)).
MATHEMATICA
f[p_, e_] := 2^Ceiling[Log2[e + 1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(n) = {my(e=logint(n + 1, 2)); if(n + 1 == 2^e, n + 1, 2^(e+1))};
a(n) = {my(f=factor(n)); prod(i=1, #f~, s(f[i, 2]))};
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Apr 28 2024
STATUS
approved