A329043 - OEIS

%I #6 Nov 08 2019 18:15:10

%S 1,2,1,1,1,8,1,1,6,2,1,3,1,2,2,1,1,3,1,48,2,2,1,5,1,2,1,6,1,128,1,1,2,

%T 2,1,3,1,2,2,10,1,8,1,6,2,2,1,7,1,3,2,6,1,1,1,320,2,2,1,12,1,2,1,1,1,

%U 8,1,6,2,8,1,3,1,2,48,6,1,8,1,21,1,2,1,3072,1,2,2,20,1,8,1,6,2,2,1,11,1,1,1,1,1,8,1,20,8

%N a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the exponent of the highest power of d dividing n.

%H Antti Karttunen, <a href="/A329043/b329043.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen, <a href="/A329043/a329043.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) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)).

%F 1+A001222(a(n)) = A329036(n).

%o (PARI)

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A329043(n) = { my(m=1,v); fordiv(A122111(n),d,if((d>1) && ((v = valuation(n,d))>0), m *= prime(v))); (m); };

%Y Cf. A001222, A008578, A122111, A286561, A329036, A329042.

%Y Cf. also A327167.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 08 2019