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 A369890 The number of divisors of the largest divisor of n whose exponents in its prime factorization are all powers of 2. 1
 1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 5, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 5, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differs from A369015 at n = 32. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000005(A353897(n)). Multiplicative with a(p^e) = A053644(e) + 1. a(n) = 2 if and only if n is prime. a(n) <= A000005(n), with equality if and only if n is in A138302. MATHEMATICA f[p_, e_] := 2^Floor[Log2[e]] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) a(n) = vecprod(apply(x -> 2^logint(x, 2) + 1, factor(n)[, 2])); CROSSREFS Cf. A000005, A000079, A053644, A138302, A353897, A369015. Sequence in context: A366901 A365551 A369015 * A334762 A358040 A305461 Adjacent sequences: A369887 A369888 A369889 * A369891 A369892 A369893 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Feb 15 2024 STATUS approved

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Last modified May 24 01:38 EDT 2024. Contains 372768 sequences. (Running on oeis4.)