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A295878 Multiplicative with a(p^(2e)) = 1, a(p^(2e-1)) = prime(e). 2

%I

%S 1,2,2,1,2,4,2,3,1,4,2,2,2,4,4,1,2,2,2,2,4,4,2,6,1,4,3,2,2,8,2,5,4,4,

%T 4,1,2,4,4,6,2,8,2,2,2,4,2,2,1,2,4,2,2,6,4,6,4,4,2,4,2,4,2,1,4,8,2,2,

%U 4,8,2,3,2,4,2,2,4,8,2,2,1,4,2,4,4,4,4,6,2,4,4,2,4,4,4,10,2,2,2,1,2,8,2,6,8,4,2,3,2,8,4,2,2,8,4,2,2,4,4,12

%N Multiplicative with a(p^(2e)) = 1, a(p^(2e-1)) = prime(e).

%C This sequence can be used as a filter. It matches at least to the following sequence, as for all i, j:

%C a(i) = a(j) => A162642(i) = A162642(j), as A162642(n) = A001222(a(n)).

%C a(i) = a(j) => A056169(i) = A056169(j), as A056169(n) = A007814(a(n)).

%C a(i) = a(j) => A295883(i) = A295883(j), as A295883(n) = A007949(a(n)).

%C a(i) = a(j) => A295662(i) = A295662(j).

%C a(i) = a(j) => A295664(i) = A295664(j).

%H Antti Karttunen, <a href="/A295878/b295878.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(1) = 1; for n>1, if n = Product prime(i)^e(i), then a(n) = Product prime((e(i)+1)/2)^A000035(e(i)).

%t Array[Apply[Times, FactorInteger[#] /. {p_, e_} /; p > 0 :> Which[p == 1, 1, EvenQ@ e, 1, True, Prime[(e + 1)/2]]] &, 120] (* _Michael De Vlieger_, Nov 29 2017 *)

%o (Scheme, with memoization-macro definec)

%o (definec (A295878 n) (if (= 1 n) 1 (let ((e (A067029 n))) (* (if (even? e) 1 (A000040 (/ (+ 1 e) 2))) (A295878 (A028234 n))))))

%Y Cf. A294873, A295879.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Nov 29 2017

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)