cp's OEIS Frontend

A351455 a(n) = A064989(A001615(A003961(n))).

%I A351455 #23 Feb 12 2022 20:30:37
%S A351455 1,1,2,2,1,2,2,4,6,1,5,4,4,2,2,8,3,6,2,2,4,5,6,8,5,4,18,4,1,2,17,16,
%T A351455 10,3,2,12,10,2,8,4,7,4,2,10,6,6,8,16,14,5,6,8,6,18,5,8,4,1,29,4,13,
%U A351455 17,12,32,4,10,4,6,12,2,31,24,3,10,10,4,10,8,10,8,54,7,12,8,3,2,2,20,25,6,8
%N A351455 a(n) = A064989(A001615(A003961(n))).
%H A351455 Antti Karttunen, <a href="/A351455/b351455.txt">Table of n, a(n) for n = 1..20000</a>
%H A351455 Antti Karttunen, <a href="/A351455/a351455.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A351455 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A351455 Multiplicative with a(p^e) = A064989((q+1)*q^(e-1)), where q = nextPrime(p) = A151800(p).
%F A351455 a(n) = A064989(A001615(A003961(n))) = A064989(A347385(A003961(n))).
%F A351455 a(n) = A003557(n) * A351450(n).
%o A351455 (PARI)
%o A351455 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A351455 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A351455 A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A351455 A351455(n) = A064989(A001615(A003961(n)));
%Y A351455 Cf. A001615, A003557, A003961, A064989, A151800, A347385, A351450.
%Y A351455 Coincides with A326042 on squarefree numbers (A005117, and apparently on no other numbers).
%Y A351455 Cf. also A351441.
%K A351455 nonn,mult
%O A351455 1,3
%A A351455 _Antti Karttunen_, Feb 12 2022