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

Author

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

Keywords

• nonn

Examples

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

Crossrefs

Composites in A384354.

Programs

Mathematica

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

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