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A353046 Odd values that are not attained by A332775(m) = m + sopf(m) - omega(m) when m runs over the natural numbers.

%I A353046 #14 Apr 22 2022 05:41:56
%S A353046 7,19,23,31,41,43,47,49,59,89,91,101,103,107,113,137,139,143,161,167,
%T A353046 169,175,179,199,209,227,229,233,239,241,243,251,259,263,271,275,281,
%U A353046 283,287,299,315,319,329,337,343,353,359,377,407,419,443,451,459,461,463,467,473,475,479,491
%N A353046 Odd values that are not attained by A332775(m) = m + sopf(m) - omega(m) when m runs over the natural numbers.
%C A353046 A332775 takes only odd values.
%C A353046 A332775(n) <= 2*n-1 and when p is prime A332775(p) = 2*p-1.
%e A353046 A332775(4) = 5, hence 5 is not a term.
%e A353046 There is no k such that A332775(k) = 7, and 7 is the least integer that is not attained, hence a(1) = 7.
%t A353046 f[n_] := n + Plus @@ (FactorInteger[n][[;;,1]] - 1); m = 500; Complement[Range[1, m, 2], Array[f, m]] (* _Amiram Eldar_, Apr 20 2022 *)
%o A353046 (PARI) f(n) = n + vecsum(factor(n)[, 1]) - omega(n); \\ A332775
%o A353046 lista(nn) = setminus(Set(select(x->(x%2), [1..nn])), Set(vector(nextprime(2*nn), k, f(k)))); \\ _Michel Marcus_, Apr 20 2022
%Y A353046 Cf. A001221 (omega), A008472 (sopf), A332775.
%K A353046 nonn
%O A353046 1,1
%A A353046 _Bernard Schott_, Apr 19 2022
%E A353046 More terms from _Michel Marcus_, Apr 20 2022