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A345892
a(n) = n + (n - 1) * (n - phi(n)).
1
1, 3, 5, 10, 9, 26, 13, 36, 33, 64, 21, 100, 25, 118, 113, 136, 33, 222, 37, 248, 201, 274, 45, 392, 145, 376, 261, 460, 57, 668, 61, 528, 449, 628, 409, 876, 73, 778, 609, 976, 81, 1272, 85, 1076, 969, 1126, 93, 1552, 385, 1520, 1001, 1480, 105, 1962, 865, 1816, 1233, 1768
OFFSET
1,2
COMMENTS
For 1 <= k <= n, add 1 if gcd(n,k) = 1, otherwise add n. For n = 9, there are 6 numbers less than or equal to 9 that are relatively prime to 9 and 3 that are not. Then a(9) = 6*1 + 9*3 = 33.
FORMULA
a(n) = Sum_{k=1..n} n^(1 - floor(1/gcd(n,k))).
MATHEMATICA
Table[n + (n - 1)*(n - EulerPhi[n]), {n, 50}]
CROSSREFS
Cf. A000010 (phi), A051953 (cototient), A345891.
Sequence in context: A069193 A078430 A372882 * A373210 A342424 A335003
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 28 2021
STATUS
approved