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A295879 Multiplicative with a(p) = 1, a(p^e) = prime(e-1) if e > 1. 2

%I

%S 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,5,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,7,1,1,

%T 1,4,1,1,1,3,1,1,1,2,2,1,1,5,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,11,1,1,1,2,

%U 1,1,1,6,1,1,2,2,1,1,1,5,5,1,1,2,1,1,1,3,1,2,1,2,1,1,1,7,1,2,2,4,1,1,1,3,1,1,1,6,1,1,1,5,1,1,1,2,2,1,1,3,2,1,1,2,3,2,1,13

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

%C This sequence can be used as a filter. It matches at least to the following sequences related to the counting of various non-unitary prime divisors:

%C For all i, j:

%C a(i) = a(j) => A056170(i) = A056170(j), as A056170(n) = A001222(a(n)).

%C a(i) = a(j) => A162641(i) = A162641(j).

%C a(i) = a(j) => A295659(i) = A295659(j).

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

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

%C a(i) = a(j) => A295884(i) = A295884(j).

%H Antti Karttunen, <a href="/A295879/b295879.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 A008578(e(i)).

%F a(n) = A064989(A181819(n)).

%t Array[Apply[Times, FactorInteger[#] /. {p_, e_} /; p > 0 :> Which[p == 1, 1, e == 1, 1, True, Prime[e - 1]]] &, 128] (* _Michael De Vlieger_, Nov 29 2017 *)

%o (Scheme, with memoization-macro definec)

%o (definec (A295879 n) (cond ((= 1 n) 1) (else (* (A008578 (A067029 n)) (A295879 (A028234 n))))))

%Y Cf. A008578, A064989, A181819.

%Y Cf. also A293515, A294875, A294895, A294897, A295878.

%Y Differs from A000688 for the first time at n=128, where a(128) = 13, while A000688(128) = 15.

%K nonn,mult

%O 1,4

%A _Antti Karttunen_, Nov 29 2017

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Last modified September 21 02:46 EDT 2020. Contains 337266 sequences. (Running on oeis4.)