cp's OEIS Frontend

A340075 The odd part of A340072(n).

%I A340075 #13 Dec 30 2020 19:59:29
%S A340075 1,1,1,3,1,1,1,9,5,3,1,3,1,5,3,27,1,5,1,9,5,3,1,9,7,1,25,15,1,3,1,81,
%T A340075 3,9,15,15,1,11,1,27,1,5,1,9,5,7,1,27,11,21,9,3,1,25,1,45,11,15,1,9,1,
%U A340075 9,25,243,3,3,1,27,7,3,1,45,1,5,21,33,15,1,1,81,125,21,1,15,9,23,15,27,1,15,5,21,9,13,33,81
%N A340075 The odd part of A340072(n).
%C A340075 Each term a(n) is a multiple of A340149(n), therefore, as both sequences have only positive terms, it follows that if a(n) = 1 then A340149(n) = 1 also, but not necessarily vice versa.
%H A340075 Antti Karttunen, <a href="/A340075/b340075.txt">Table of n, a(n) for n = 1..8191</a>
%H A340075 Antti Karttunen, <a href="/A340075/a340075.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A340075 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A340075 a(n) = A000265(A340072(n)).
%F A340075 a(n) = A339904(n) / A340074(n) = A339904(n) / gcd(A003961(n)-1, A339904(n)).
%F A340075 For all n >= 0, a(A019565(n)) = A339901(n).
%o A340075 (PARI)
%o A340075 A000265(n) = (n>>valuation(n,2));
%o A340075 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A340075 A340072(n) = { my(x=A003961(n), u=eulerphi(x)); u/gcd(x-1, u); };
%o A340075 A340075(n) = A000265(A340072(n));
%Y A340075 Cf. A000265, A003961, A019565, A339901, A339904, A340072, A340074, A340076 (positions of ones), A340149 (differs from the first time at n=85).
%K A340075 nonn
%O A340075 1,4
%A A340075 _Antti Karttunen_, Dec 28 2020