A361469 - OEIS

%I #10 Mar 21 2023 09:23:00

%S 0,3,3,3,4,4,4,7,3,7,3,4,4,5,7,6,4,6,5,7,7,6,4,6,4,5,7,5,6,8,3,9,6,7,

%T 8,6,4,6,7,11,4,8,6,4,7,5,5,7,4,5,5,3,5,8,5,9,8,9,3,8,4,6,7,7,8,7,6,7,

%U 5,9,3,8,6,5,7,6,7,8,5,10,6,7,5,6,8,7,9,10,4,10,8,5,6,6,9,10,4,7,6,5,5,6,6,7,11

%N a(n) = bigomega(A249670(A003961(n))).

%C Conjecture: There are no 1's in this sequence. If true, it would imply that there are no odd terms in A065997.

%C The first n with a(n) = 2 is 1684804. Note that A003961(1684804) = 5659641 is so far the only known odd term in A247086.

%H Antti Karttunen, <a href="/A361469/b361469.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A361469/a361469.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A001222(A361468(n)) = A001222(A249670(A003961(n))).

%o (PARI)

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

%o A249670(n) = { my(ab = sigma(n)/n); numerator(ab)*denominator(ab); };

%o A361469(n) = bigomega(A249670(A003961(n)));

%Y Cf. A001222, A003961, A065997, A247086, A249670, A361468.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 20 2023