cp's OEIS Frontend

A351449 a(n) = A064989(A295294(A003961(n))).

%I A351449 #14 Feb 12 2022 20:30:12
%S A351449 1,1,1,11,1,1,1,3,29,1,1,11,1,1,1,49,1,29,1,11,1,1,1,3,34,1,22,11,1,1,
%T A351449 1,55,1,1,1,319,1,1,1,3,1,1,1,11,29,1,1,49,85,34,1,11,1,22,1,3,1,1,1,
%U A351449 11,1,1,29,1091,1,1,1,11,1,1,1,87,1,1,34,11,1,1,1,49,469,1,1,11,1,1,1,3,1
%N A351449 a(n) = A064989(A295294(A003961(n))).
%H A351449 Antti Karttunen, <a href="/A351449/b351449.txt">Table of n, a(n) for n = 1..20000</a>
%H A351449 Antti Karttunen, <a href="/A351449/a351449.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A351449 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A351449 Multiplicative with a(p) = 1 and for e > 1, a(p^e) = A064989((q^(e+1)-1)/(q-1)), where q = nextPrime(p) = A151800(p).
%F A351449 a(n) = A064989(A295294(A003961(n))) = A326042(A057521(n)).
%F A351449 a(n) = A326042(n) / A351451(n).
%o A351449 (PARI)
%o A351449 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A351449 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A351449 A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521
%o A351449 A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A351449 A295294(n) = sigma(A057521(n));
%o A351449 A351449(n) = A064989(A295294(A003961(n)));
%Y A351449 Cf. A003961, A048250, A057521, A064989, A151800, A295294, A326042, A351450, A351451.
%K A351449 nonn,mult
%O A351449 1,4
%A A351449 _Antti Karttunen_, Feb 11 2022