A345890 a(n) = n + (n - 1) * (n - pi(n)).

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.

Links

Table of n, a(n) for n=1..54.

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

Adjacent sequences: A345887 A345888 A345889 * A345891 A345892 A345893

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 28 2021

Status

approved