A395458 - OEIS

%I #6 May 11 2026 17:43:43

%S 1,2,2,6,2,4,2,18,11,4,2,28,2,4,4,50,2,40,2,44,4,4,2,100,27,4,56,60,2,

%T 8,2,130,4,4,4,184,2,4,4,164,2,8,2,92,94,4,2,292,51,104,4,108,2,220,4,

%U 228,4,4,2,248,2,4,130,322,4,8,2,140,4,8,2,580,2,4,154,156,4,8,2,484,245,4,2,344,4,4,4,356

%N a(n) = n*tau(n) - (n-1)*tau(rad(n)).

%C For each divisor d of n add 1 if gcd(d,n/d) = 1, else add n.

%F a(n) = Sum_{d|n} n^(1 - [gcd(d,n/d) = 1]), where [ ] is the Iverson bracket.

%F a(p^k) = p^k*(k-1)+2 for p prime and k>=1. - _Wesley Ivan Hurt_, May 11 2026

%e a(12) = 12^0 + 12^1 + 12^0 + 12^0 + 12^1 + 12^0 = 28.

%t Table[Sum[n^(1 - KroneckerDelta[GCD[d, n/d], 1]), {d, Divisors[n]}], {n, 100}]

%Y Cf. A000005 (tau), A007947 (rad), A034444, A395435.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, Apr 23 2026