OFFSET
1,1
COMMENTS
Conjecture: the asymptotic density of terms is equal to 0 and this sequence is infinite.
LINKS
Kevin P. Thompson, Table of n, a(n) for n = 1..288
EXAMPLE
a(1) = 4365 because the divisors of 4365 are: 1, 3, 5, 9, 15, 45, 97, 291, 485, 873, 1455, 4365; so, tau(4365) = 12 and sigma(4365) = 7644. The divisors of 4364 are: 1, 2, 4, 1091, 2182, 4364; so, tau(4364) = 6 and sigma(4364) = 7644. Thus tau(4365) = 2*tau(4364), sigma(4365) = sigma(4364) and so 4365 is a term.
MATHEMATICA
Select[Range[2, 10^6], DivisorSigma[0, #] == 2*DivisorSigma[0, # - 1] && DivisorSigma[1, #] == DivisorSigma[1, # - 1] &] (* Amiram Eldar, Sep 08 2021 *)
PROG
(PARI) for(k=2, 100000000, if(numdiv(k)==2*numdiv(k-1) && sigma(k)==sigma(k-1), print1(k", ")))
(Python) from sympy import divisor_count as tau, divisor_sigma as sigma
print([k for k in range(2, 10**6) if tau(k) == 2*tau(k-1) and sigma(k) == sigma(k-1)]) # Karl-Heinz Hofmann, Jan 15 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Claude H. R. Dequatre, Sep 08 2021
STATUS
approved