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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
OFFSET
1,1
COMMENTS
A332775 takes only odd values.
A332775(n) <= 2*n-1 and when p is prime A332775(p) = 2*p-1.
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
KEYWORD
nonn
AUTHOR
Bernard Schott, Apr 19 2022
EXTENSIONS
More terms from Michel Marcus, Apr 20 2022
STATUS
approved