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A347603 Numbers k such that tau(k) = 2*tau(k-1) and sigma(k) = sigma(k-1), where tau(k) and sigma(k) are respectively the number and sum functions of the divisors of k. 3
4365, 74919, 79827, 111507, 347739, 445875, 739557, 2168907, 4481986, 7263945, 7845387, 9309465, 10838247, 12290055, 12673095, 18151479, 22083215, 25645707, 39175955, 62634519, 69076995, 72794967, 80889207, 81166839, 87215967, 94682133, 107522943, 110768835, 119192283 (list; graph; refs; listen; history; text; internal format)
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

Cf. A027750, A000005, A000203.

Similar sequences: A002961, A005237, A005238, A006601, A049051, A347076.

Sequence in context: A164517 A125825 A031564 * A217345 A140937 A327789

Adjacent sequences: A347600 A347601 A347602 * A347604 A347605 A347606

KEYWORD

nonn,easy

AUTHOR

Claude H. R. Dequatre, Sep 08 2021

STATUS

approved

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Last modified February 4 20:58 EST 2023. Contains 360082 sequences. (Running on oeis4.)