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

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.

Links

Table of n, a(n) for n=1..60.

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