A062955 -id:A062955 - cp's OEIS frontend

A345891 a(n) = n + (n - 1) * phi(n).

1, 3, 7, 10, 21, 16, 43, 36, 57, 46, 111, 56, 157, 92, 127, 136, 273, 120, 343, 172, 261, 232, 507, 208, 505, 326, 495, 352, 813, 262, 931, 528, 673, 562, 851, 456, 1333, 704, 951, 664, 1641, 534, 1807, 904, 1101, 1036, 2163, 800, 2065, 1030, 1651, 1276, 2757, 1008, 2215, 1376

Offset: 1

Wesley Ivan Hurt, Jun 28 2021

nonn

For 1 <= k <= n, add n if gcd(n,k) = 1, otherwise add 1. For n = 9 there are 6 numbers less than or equal to 9 that are relatively prime to 9 and 3 that are not. So a(9) = 9*6 + 3*1 = 57.

Cf. A000010 (phi), A062955, A345892.

Mathematica
```
Table[n + (n - 1)*EulerPhi[n], {n, 50}]
```

a(n) = n + (n-1)*eulerphi(n); \\ Michel Marcus, Jun 28 2021

a(n) = Sum_{k=1..n} n^floor(1/gcd(n,k)).

a(n) = A062955(n) + n. - Michel Marcus, Jun 28 2021

A309106 Triangular array T(m,n): number of sequences of n residues modulo m such that no nonempty subsequence sums to zero, for m>=1, n=0..m-1.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 6, 2, 1, 4, 12, 16, 4, 1, 5, 20, 44, 10, 2, 1, 6, 30, 96, 90, 36, 6, 1, 7, 42, 174, 240, 84, 28, 4, 1, 8, 56, 288, 690, 336, 168, 48, 6, 1, 9, 72, 440, 1344, 984, 336, 144, 36, 4, 1, 10, 90, 640, 2590, 3060, 2100, 1200, 450, 100, 10

Offset: 1

Max Alekseyev, Jul 12 2019

T(m,n)=0 if n>=m.

Brendan McKay et al., probability of zero subset sum, MathOverflow, 2013.

Columns: A000012 (n=0), A000027 (n=1), A002378 (n=2).

Diagonals: A000010 (n=m-1), A062955 (n=m-2, starting with m=4).

cp's OEIS Frontend

A345891 a(n) = n + (n - 1) * phi(n).

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