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

Author

Bernard Schott, Apr 19 2022

Keywords

• nonn

Comments

A332775 takes only odd values.

A332775(n) <= 2*n-1 and when p is prime A332775(p) = 2*p-1.

Examples

			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.
		

Crossrefs

Cf. A001221 (omega), A008472 (sopf), A332775.

Programs

Mathematica

f[n_] := n + Plus @@ (FactorInteger[n][[;;,1]] - 1); m = 500; Complement[Range[1, m, 2], Array[f, m]] (* Amiram Eldar, Apr 20 2022 *)

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

Extensions

More terms from Michel Marcus, Apr 20 2022