A023897 sigma_1(n) / phi(n) for balanced numbers.

1, 3, 2, 6, 7, 4, 3, 9, 2, 8, 5, 6, 7, 4, 7, 10, 5, 12, 4, 9, 10, 3, 4, 14, 10, 8, 6, 13, 9, 8, 5, 15, 7, 2, 6, 8, 4, 5, 12, 6, 7, 10, 10, 11, 14, 12, 9, 4, 3, 4, 12, 9, 4, 4, 7, 5, 7, 10, 3, 5, 4, 13, 14, 12, 10, 9, 10, 8, 7, 4, 8, 6, 18, 9, 3, 8, 13, 8, 15, 15, 8, 3, 14, 9, 10, 8, 8, 10, 5, 7, 8, 11, 6, 11, 13, 6

Offset

1,2

Comments

sigma_1(n) is the sum of the divisors of n [same as sigma(n)] (A000203).

Links

Jud McCranie, Table of n, a(n) for n = 1..10000 (first 800 terms from Vincenzo Librandi)

Mathematica

Select[ Array[ DivisorSigma[ 1, # ]/EulerPhi[ # ]&, 20000 ], IntegerQ ]

Prog

(Magma) [ q: n in [1..20000] | r eq 0 where q, r is Quotrem(SumOfDivisors(n), EulerPhi(n)) ]; // Klaus Brockhaus, Nov 09 2008
(Python)
from math import prod
from itertools import count, islice
from sympy import factorint
def A023897_gen(startvalue=1): # generator of terms >= startvalue
    for m in count(max(startvalue, 1)):
        f = factorint(m)
        q, r = divmod(prod(p**(e+2)-p for p, e in f.items()), m*prod((p-1)**2 for p in f))
        if not r:
            yield q
A023897_list = list(islice(A023897_gen(), 20)) # Chai Wah Wu, Aug 12 2024

Crossrefs

Cf. A000010, A000203, A020492.

Sequence in context: A196518 A207636 A125764 * A267100 A178754 A276446

Adjacent sequences: A023894 A023895 A023896 * A023898 A023899 A023900

Keyword

nonn

Author

Olivier Gérard

Status

approved