VOOZH about

URL: https://oeis.org/A345890

⇱ A345890 - OEIS

login
A345890
a(n) = n + (n - 1) * (n - pi(n)).
1
1, 3, 5, 10, 13, 21, 25, 36, 49, 64, 71, 89, 97, 118, 141, 166, 177, 205, 217, 248, 281, 316, 331, 369, 409, 451, 495, 541, 561, 610, 631, 683, 737, 793, 851, 911, 937, 1000, 1065, 1132, 1161, 1231, 1261, 1334, 1409, 1486, 1519, 1599, 1681, 1765, 1851, 1939, 1977, 2068
OFFSET
1,2
COMMENTS
For all 1 <= k <= n, add 1 if k is prime, otherwise add n. For example, when n = 7, there are 4 numbers less than or equal to 7 that are prime and 3 that are not. Then a(7) = 1*4 + 7*3 = 25.
FORMULA
a(n) = Sum_{k=1..n} n^c(n), where c(n) is the characteristic function of nonprimes (A005171).
MATHEMATICA
Table[n + (n - 1)*(n - PrimePi[n]), {n, 50}]
CROSSREFS
Cf. A000720 (pi), A005171, A345888.
Sequence in context: A165718 A340528 A031878 * A265282 A160792 A308759
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 28 2021
STATUS
approved