A342656 - OEIS

%I #16 Jan 29 2022 20:14:58

%S 0,0,1,0,1,0,1,1,2,0,1,0,1,1,2,0,1,0,1,2,2,0,1,1,2,1,2,0,2,0,1,1,2,1,

%T 3,0,1,2,2,0,1,0,1,1,4,0,1,1,2,2,1,0,1,2,1,2,3,0,1,0,2,1,3,1,2,0,2,1,

%U 1,0,2,0,2,1,2,1,2,0,1,2,2,0,3,2,3,4,4,0,3,2,2,3,4,2,2,0,2,2,2,0,3,0,1,2

%N a(n) = A087436(A156552(n)); Number of odd prime factors in A156552(n), counted with repetitions.

%H Antti Karttunen, <a href="/A342656/b342656.txt">Table of n, a(n) for n = 2..10000</a> (based on Hans Havermann's factorization of A156552)

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

%F a(n) = A087436(A156552(n)) = A001222(A322993(n)).

%F a(n) = A342655(2*A246277(n)) = 1 + A342655(n) - A055396(n).

%F a(p) = 0 for all primes p.

%F a(A003961(n)) = a(n).

%o (PARI)

%o A087436(n) = (bigomega(n>>valuation(n,2)));

%o A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};

%o A342656(n) = A087436(A156552(n));

%o (PARI)

%o \\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt

%o v156552sigs = readvec("a156552.txt");

%o A342656(n) = if(2==n,0,my(prsig=v156552sigs[n],ps=prsig[1],es=prsig[2]); vecsum(es)-((2==ps[1])*es[1])); \\ _Antti Karttunen_, Jan 29 2022

%Y Cf. A000265, A001222, A003961, A055396, A087436, A156552, A246277, A322993, A342655.

%Y Cf. also A324117, A324118.

%K nonn

%O 2,9

%A _Antti Karttunen_, Mar 18 2021