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Numbers n such that tau(n+1) - tau(n) = -2, where tau(n) = the number of divisors of n (A000005).
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%I #13 Oct 06 2017 01:05:11

%S 6,10,20,22,32,45,46,50,58,68,76,82,92,106,117,124,152,166,170,174,

%T 178,212,226,236,261,262,272,325,333,338,346,358,382,405,412,424,435,

%U 436,452,464,466,474,477,478,495,502,506,512,530,555,562,567,574,578,586

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

%C 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.

%C 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_k-1) = -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.

%H Jaroslav Krizek, <a href="/A227874/b227874.txt">Table of n, a(n) for n = 1..2000</a>

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

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

%Y Cf. A000005.

%Y Cf. A055927 (numbers n such that tau(n+1) - tau(n) = 1).

%Y Cf. A230115 (numbers n such that tau(n+1) - tau(n) = 2).

%Y Cf. A230653 (numbers n such that tau(n+1) - tau(n) = 3).

%Y Cf. A230654 (numbers n such that tau(n+1) - tau(n) = 4).

%Y Cf. A228453 (numbers n such that tau(n+1) - tau(n) = 5).

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Nov 03 2013