A360327 a(n) is the sum of divisors of n that have only prime-indexed prime factors.

1, 1, 4, 1, 6, 4, 1, 1, 13, 6, 12, 4, 1, 1, 24, 1, 18, 13, 1, 6, 4, 12, 1, 4, 31, 1, 40, 1, 1, 24, 32, 1, 48, 18, 6, 13, 1, 1, 4, 6, 42, 4, 1, 12, 78, 1, 1, 4, 1, 31, 72, 1, 1, 40, 72, 1, 4, 1, 60, 24, 1, 32, 13, 1, 6, 48, 68, 18, 4, 6, 1, 13, 1, 1, 124, 1, 12

Offset

1,3

Comments

Equivalently, a(n) is the sum of divisors of the largest divisor of n that has only prime-indexed prime factors.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = 1 if and only if n is in A320628.

a(n) = A000203(n) if and only if n is in A076610.

a(n) = A000203(A360325(n)).

Multiplicative with a(p^e) = (p^(e+1)-1)/(p-1) if p is a prime-indexed prime (A006450), and 1 otherwise.

Mathematica

f[p_, e_] := If[PrimeQ[PrimePi[p]], (p^(e+1)-1)/(p-1), 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(isprime(primepi(p[i])), (p[i]^(e[i]+1)-1)/(p[i]-1), 1)); }

Crossrefs

Cf. A000203, A006450, A076610, A320628, A360325, A360326.

Sequence in context: A127556 A227832 A293432 * A050307 A248416 A348853

Adjacent sequences: A360324 A360325 A360326 * A360328 A360329 A360330

Keyword

nonn,mult

Author

Amiram Eldar, Feb 03 2023

Status

approved