A340075 - OEIS

%I #13 Dec 30 2020 19:59:29

%S 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 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 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 The odd part of A340072(n).

%C 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 Antti Karttunen, <a href="/A340075/b340075.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A340075/a340075.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A000265(A340072(n)).

%F a(n) = A339904(n) / A340074(n) = A339904(n) / gcd(A003961(n)-1, A339904(n)).

%F For all n >= 0, a(A019565(n)) = A339901(n).

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A340072(n) = { my(x=A003961(n), u=eulerphi(x)); u/gcd(x-1, u); };

%o A340075(n) = A000265(A340072(n));

%Y Cf. A000265, A003961, A019565, A339901, A339904, A340072, A340074, A340076 (positions of ones), A340149 (differs from the first time at n=85).

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 28 2020