A331312 - OEIS

%I #8 Jan 21 2020 18:22:56

%S 1,1,2,1,8,2,128,1,3,8,32768,2,2147483648,128,16,1,

%T 9223372036854775808,3,170141183460469231731687303715884105728,8,256,

%U 32768,57896044618658097711785492504343953926634992332820282019728792003956564819968,2,27,2147483648,6,128

%N a(n) = A225546(n) / A293442(n).

%H Antti Karttunen, <a href="/A331312/b331312.txt">Table of n, a(n) for n = 1..40</a>

%F a(n) = A225546(n) / A293442(n).

%F Multiplicative, with a(prime(i)^j) = A019565(j)^A000225(i-1).

%o (PARI)

%o A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

%o A331312(n) = { my(f=factor(n)); for (i=1, #f~, my(p=f[i, 1]); f[i, 1] = A019565(f[i, 2]); f[i, 2] = (2^(primepi(p)-1))-1; ); factorback(f); };

%Y Cf. A000225, A019565, A225546, A293442, A331311.

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, Jan 21 2020