A351451 - OEIS

%I #14 Feb 12 2022 20:30:22

%S 1,1,2,1,1,2,2,1,1,1,5,2,4,2,2,1,3,1,2,1,4,5,6,2,1,4,1,2,1,2,17,1,10,

%T 3,2,1,10,2,8,1,7,4,2,5,1,6,8,2,1,1,6,4,6,1,5,2,4,1,29,2,13,17,2,1,4,

%U 10,4,3,12,2,31,1,3,10,2,2,10,8,10,1,1,7,12,4,3,2,2,5,25,1,8,6,34,8,2

%N a(n) = A064989(A092261(A003961(n))).

%H Antti Karttunen, <a href="/A351451/b351451.txt">Table of n, a(n) for n = 1..20000</a>

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

%F Multiplicative with a(p) = A064989(q+1) and a(p^e) = 1 for e > 1, where q = nextPrime(p) = A151800(p).

%F a(n) = A351450(A055231(n)) = A064989(A092261(A003961(n))).

%F a(n) = A326042(n) / A351449(n).

%o (PARI)

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

%o A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));

%o A055231(n) = {my(f=factor(n)); for (k=1, #f~, if (f[k, 2] > 1, f[k, 2] = 0); ); factorback(f); } \\ From A055231

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

%o A351450(n) = A064989(A048250(A003961(n)));

%o A351451(n) = A351450(A055231(n));

%Y Cf. A003961, A048250, A055231, A064989, A092261, A151800, A351449, A351450.

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, Feb 11 2022