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A322584 a(n) is the number of terms of A025487 that divide n.

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%I A322584 #14 Jan 01 2024 08:00:31
%S A322584 1,2,1,3,1,3,1,4,1,2,1,5,1,2,1,5,1,3,1,3,1,2,1,7,1,2,1,3,1,4,1,6,1,2,
%T A322584 1,6,1,2,1,4,1,3,1,3,1,2,1,9,1,2,1,3,1,3,1,4,1,2,1,7,1,2,1,7,1,3,1,3,
%U A322584 1,2,1,9,1,2,1,3,1,3,1,5,1,2,1,5,1,2,1,4,1,4,1,3,1,2,1,11,1,2,1,3,1,3,1,4,1
%N A322584 a(n) is the number of terms of A025487 that divide n.
%H A322584 Antti Karttunen, <a href="/A322584/b322584.txt">Table of n, a(n) for n = 1..20000</a>
%H A322584 Antti Karttunen, <a href="/A322584/a322584.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A322584 a(n) = Sum_{d|} A322585(d).
%F A322584 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A161360 = 2.495806... . - _Amiram Eldar_, Jan 01 2024
%o A322584 (PARI)
%o A322584 A322585(n) = { my(f = factor(n)); for(i=1,#f~,if((primepi(f[i,1])!=i)||((i>1)&&(f[i-1,2]<f[i,2])),return(0))); (1); };
%o A322584 A322584(n) = sumdiv(n,d,A322585(d));
%Y A322584 Inverse Möbius transform of A322585.
%Y A322584 Cf. A025487, A161360.
%Y A322584 Cf. also A181801.
%K A322584 nonn
%O A322584 1,2
%A A322584 _Antti Karttunen_, Dec 20 2018