A351395 Sum of the divisors of n that are either squarefree, prime powers, or both.

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 16, 14, 24, 24, 31, 18, 21, 20, 22, 32, 36, 24, 24, 31, 42, 40, 28, 30, 72, 32, 63, 48, 54, 48, 25, 38, 60, 56, 30, 42, 96, 44, 40, 33, 72, 48, 40, 57, 43, 72, 46, 54, 48, 72, 36, 80, 90, 60, 76, 62, 96, 41, 127, 84, 144, 68, 58, 96, 144, 72

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{d|n} d * sign(mu(d)^2 + [omega(d) = 1]).

Example

a(36) = 25; 36 has 4 squarefree divisors 1,2,3,6 (where the primes 2 and 3 are both squarefree and 1st powers of primes) and 2 (additional) divisors that are powers of primes, 2^2 and 3^2. The sum of the divisors is then 1+2+3+4+6+9 = 25.

Mathematica

Array[DivisorSum[#, #*Sign[MoebiusMu[#]^2 + Boole[PrimeNu[#] == 1]] &] &, 71] (* Michael De Vlieger, Feb 10 2022 *)

Prog

(PARI) a(n) = sumdiv(n, d, if (issquarefree(d) || isprimepower(d), d)); \\ Michel Marcus, Feb 10 2022

Crossrefs

Cf. A001221, A008683, A246655.

Sums of divisors: A048250 (squarefree), A023889 (prime powers), A008472 (prime).

Sequence in context: A034690 A069192 A076887 * A140782 A284587 A097011

Adjacent sequences: A351392 A351393 A351394 * A351396 A351397 A351398

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 09 2022

Status

approved