

A227874


Numbers n such that tau(n+1)  tau(n) = 2, where tau(n) = the number of divisors of n (A000005).


2



6, 10, 20, 22, 32, 45, 46, 50, 58, 68, 76, 82, 92, 106, 117, 124, 152, 166, 170, 174, 178, 212, 226, 236, 261, 262, 272, 325, 333, 338, 346, 358, 382, 405, 412, 424, 435, 436, 452, 464, 466, 474, 477, 478, 495, 502, 506, 512, 530, 555, 562, 567, 574, 578, 586
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OFFSET

1,1


COMMENTS

Numbers n such that tau(n)  tau(n+1) = 2. Numbers n such that A051950(n+1) = 2. Numbers n such that A049820(n)  A049820(n+1) = 3.
Sequence of starts of first run of n (n>=2) consecutive integers m_1, m_2, ..., m_n such that tau(m_k)  tau(m_k1) = 2, for all k=n...2: 6, 45, 1016, ... (a(5) > 100000); example for n=4: tau(1016) = 8, tau(1017) = 6, tau(1018) = 4, tau(1019) = 2.


LINKS

Jaroslav Krizek, Table of n, a(n) for n = 1..2000


EXAMPLE

45 is in sequence because tau(46)  tau(45) = 4  6 = 2.


MATHEMATICA

Select[ Range[ 50000], DivisorSigma[0, # ]  2 == DivisorSigma[0, # + 1] &]


CROSSREFS

Cf. A000005.
Cf. A055927 (numbers n such that tau(n+1)  tau(n) = 1).
Cf. A230115 (numbers n such that tau(n+1)  tau(n) = 2).
Cf. A230653 (numbers n such that tau(n+1)  tau(n) = 3).
Cf. A230654 (numbers n such that tau(n+1)  tau(n) = 4).
Cf. A228453 (numbers n such that tau(n+1)  tau(n) = 5).
Sequence in context: A270306 A327410 A145351 * A015783 A300020 A068017
Adjacent sequences: A227871 A227872 A227873 * A227875 A227876 A227877


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Nov 03 2013


STATUS

approved



