A340149 - OEIS

%I #9 Dec 30 2020 20:00:40

%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 9,25,243,3,3,1,27,7,3,1,45,1,5,21,33,15,1,1,81,125,21,1,15,3,23,15,27,1,15,5,21,9,13,33

%N Odd part of A340147: a(n) = A000265(A247074(A003961(n))).

%C Each term a(n) is a divisor of A340075(n), at n=85 occurs the first proper divisor.

%H Antti Karttunen, <a href="/A340149/b340149.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A340149/a340149.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(A340147(n)) = A000265(A247074(A003961(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 A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074

%o A340149(n) = A000265(A247074(A003961(n)));

%Y Cf. A000265, A003961, A247074, A340147, A340150 (positions of ones).

%Y Differs from related A340075 for the first time at n=85, where a(85) = 3, while A340075(85) = 9.

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 30 2020