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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. 1
 7, 19, 23, 31, 41, 43, 47, 49, 59, 89, 91, 101, 103, 107, 113, 137, 139, 143, 161, 167, 169, 175, 179, 199, 209, 227, 229, 233, 239, 241, 243, 251, 259, 263, 271, 275, 281, 283, 287, 299, 315, 319, 329, 337, 343, 353, 359, 377, 407, 419, 443, 451, 459, 461, 463, 467, 473, 475, 479, 491 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A332775 takes only odd values. A332775(n) <= 2*n-1 and when p is prime A332775(p) = 2*p-1. LINKS EXAMPLE A332775(4) = 5, hence 5 is not a term. There is no k such that A332775(k) = 7, and 7 is the least integer that is not attained, hence a(1) = 7. MATHEMATICA f[n_] := n + Plus @@ (FactorInteger[n][[;; , 1]] - 1); m = 500; Complement[Range[1, m, 2], Array[f, m]] (* Amiram Eldar, Apr 20 2022 *) PROG (PARI) f(n) = n + vecsum(factor(n)[, 1]) - omega(n); \\ A332775 lista(nn) = setminus(Set(select(x->(x%2), [1..nn])), Set(vector(nextprime(2*nn), k, f(k)))); \\ Michel Marcus, Apr 20 2022 CROSSREFS Cf. A001221 (omega), A008472 (sopf), A332775. Sequence in context: A113972 A082422 A129812 * A032680 A141831 A176182 Adjacent sequences:  A353043 A353044 A353045 * A353047 A353048 A353049 KEYWORD nonn AUTHOR Bernard Schott, Apr 19 2022 EXTENSIONS More terms from Michel Marcus, Apr 20 2022 STATUS approved

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Last modified August 7 14:56 EDT 2022. Contains 355989 sequences. (Running on oeis4.)