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A350073 a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.

%I A350073 #14 Dec 15 2021 21:43:57
%S A350073 1,2,1,5,2,2,1,6,11,4,2,5,5,2,2,29,4,22,3,10,1,4,2,6,29,10,3,5,6,4,1,
%T A350073 20,2,8,2,55,17,6,5,12,10,2,7,10,22,4,2,29,34,58,4,25,8,6,4,6,3,12,6,
%U A350073 10,29,2,11,113,10,4,13,20,2,4,4,66,31,34,29,15,2,10,3,58,49,20,10,5,8,14,6,12,12,44,5,10
%N A350073 a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
%H A350073 Antti Karttunen, <a href="/A350073/b350073.txt">Table of n, a(n) for n = 1..20000</a>
%H A350073 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A350073 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A350073 Multiplicative with a(p^e) = A064989(1 + p + p^2 + ... + p^e).
%F A350073 a(n) = A064989(A000203(n)) = A064989(A161942(n)).
%t A350073 f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[DivisorSigma[1, n]]; Array[a, 100] (* _Amiram Eldar_, Dec 12 2021 *)
%o A350073 (PARI)
%o A350073 A064989(n) = { my(f = factor(n)); for (i=1, #f~, f[i,1] = if(2==f[i, 1],1,precprime(f[i, 1]-1))); factorback(f); };
%o A350073 A350073(n) = A064989(sigma(n));
%Y A350073 Cf. A000203, A064989, A161942, A337343 (a(n) >= n), A348748, A348749.
%Y A350073 Cf. also A326042, A350072.
%K A350073 nonn,mult
%O A350073 1,2
%A A350073 _Antti Karttunen_, Dec 12 2021