A384493 Composite integers k such that sigma(k) | (k + 1)*tau(k) where tau is number of divisors of k.

20, 35, 104, 207, 399, 464, 650, 1519, 1952, 2015, 2774, 2915, 2975, 4454, 11339, 22847, 32318, 63503, 97019, 122499, 130304, 352835, 522752, 924482, 1949375, 7366463, 8382464, 9486399, 15857855, 30222023, 39992975, 49280399, 63483104, 65094623, 69291935, 95309054

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

104 is in the sequence as tau(104) = 8, sigma(104) = 210 and sigma(104) = 210 | 840 = (104 + 1) * 8 = (104 + 1) * tau(104).

Mathematica

Select[Range[4, 2^20], And[CompositeQ[#1], Divisible[(#1 + 1)*#2, #3]] & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* Michael De Vlieger, May 31 2025 *)

Prog

(PARI) is(n) = my(f = factor(n), nd = numdiv(f)); nd > 2 && ((n+1)*nd) % sigma(f) == 0
(Python)
from sympy import divisors, isprime
def ok(n): return n > 3 and not isprime(n) and (n+1)*len(d:=divisors(n))%sum(d) == 0
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, May 31 2025

Crossrefs

Composites in A384354.

Sequence in context: A255349 A254363 A229356 * A048066 A287055 A326403

Adjacent sequences: A384490 A384491 A384492 * A384494 A384495 A384496

Keyword

nonn

Author

David A. Corneth and Ivan N. Ianakiev, May 31 2025

Status

approved