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A293442 Multiplicative with a(p^e) = A019565(e). 20
1, 2, 2, 3, 2, 4, 2, 6, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 12, 3, 4, 6, 6, 2, 8, 2, 10, 4, 4, 4, 9, 2, 4, 4, 12, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 12, 4, 12, 4, 4, 2, 12, 2, 4, 6, 15, 4, 8, 2, 6, 4, 8, 2, 18, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4, 4, 12, 2, 12, 4, 6, 4, 4, 4, 20, 2, 6, 6, 9, 2, 8, 2, 12, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(1) = 1; for n > 1, a(n) = A019565(A067029(n)) * a(A028234(n)).

Other identities. For all n >= 1:

a(a(n)) = A293444(n).

A048675(a(n)) = A001222(n).

A001222(a(n)) = A064547(n) = A048675(A293444(n)).

A007814(a(n)) = A162642(n).

A087207(a(n)) = A267116(n).

A248663(a(n)) = A268387(n).

MATHEMATICA

f[n_] := If[n == 1, 1, Apply[Times, Prime@ Flatten@ Position[Reverse@ IntegerDigits[Last@ #, 2], 1]] * f[n/Apply[Power, #]] &@ FactorInteger[n][[1]]]; Array[f, 105] (* Michael De Vlieger, Oct 31 2017 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A293442 n) (if (= 1 n) n (* (A019565 (A067029 n)) (A293442 (A028234 n)))))

CROSSREFS

Cf. A019565, A028234, A067029.

Cf. also A293214, A293443, A293444.

Sequence in context: A296073 A317943 A305800 * A318470 A175501 A144370

Adjacent sequences:  A293439 A293440 A293441 * A293443 A293444 A293445

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Oct 31 2017

STATUS

approved

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Last modified January 22 16:29 EST 2020. Contains 331152 sequences. (Running on oeis4.)