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A339776
Numbers m such that tau(m) = tau(m + 1) - 1 = tau(m + 2), where tau(k) = the number of divisors of k (A000005).
2
3, 252003, 293763, 770883, 1444803, 2630883, 6543363, 8421603, 9375843, 18992163, 19731363, 21883683, 22108803, 25786083, 25989603, 32512803, 35259843, 48972003, 98049603, 101566083, 132204003, 155201763, 160224963, 162766563, 187197123, 208455843, 291658083
OFFSET
1,1
COMMENTS
Corresponding values of tau(a(n)): 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, ...
Triplets of [tau(a(n)), tau(a(n) + 1), tau(a(n) + 2)] = [tau(a(n)), tau(a(n)) + 1, tau(a(n))]: [2, 3, 2], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], ...
a(n) is one less than a perfect square. - David A. Corneth, Dec 29 2020
LINKS
EXAMPLE
tau(3) = 2, tau(4) = 3, tau(5) = 2.
MATHEMATICA
d1 = 1; d2 = 2; s = {}; Do[d3 = DivisorSigma[0, n]; If[Equal @@ {d1, d2 - 1, d3}, AppendTo[s, n - 2]]; d1 = d2; d2 = d3, {n, 3, 10^7}]; s (* Amiram Eldar, Dec 17 2020 *)
PROG
(Magma) [m: m in [2..10^6] | #Divisors(m + 1) - 1 eq #Divisors(m) and #Divisors(m + 2) eq #Divisors(m)]
(PARI) isok(m) = my(nb = numdiv(m)); (numdiv(m+2) == nb) && (numdiv(m+1) == nb+1); \\ Michel Marcus, Dec 18 2020
CROSSREFS
Subsequence of A005563.
Intersection of A062832 and A055927.
Sequence in context: A250495 A317168 A176586 * A033982 A326618 A366680
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 16 2020
EXTENSIONS
More terms from Amiram Eldar, Dec 16 2020
STATUS
approved