cp's OEIS Frontend

A227874 Numbers n such that tau(n+1) - tau(n) = -2, where tau(n) = the number of divisors of n (A000005).

%I A227874 #13 Oct 06 2017 01:05:11
%S A227874 6,10,20,22,32,45,46,50,58,68,76,82,92,106,117,124,152,166,170,174,
%T A227874 178,212,226,236,261,262,272,325,333,338,346,358,382,405,412,424,435,
%U A227874 436,452,464,466,474,477,478,495,502,506,512,530,555,562,567,574,578,586
%N A227874 Numbers n such that tau(n+1) - tau(n) = -2, where tau(n) = the number of divisors of n (A000005).
%C A227874 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 A227874 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 A227874 Jaroslav Krizek, <a href="/A227874/b227874.txt">Table of n, a(n) for n = 1..2000</a>
%e A227874 45 is in sequence because tau(46) - tau(45) = 4 - 6 = -2.
%t A227874 Select[ Range[ 50000], DivisorSigma[0, # ] - 2 == DivisorSigma[0, # + 1] &]
%Y A227874 Cf. A000005.
%Y A227874 Cf. A055927 (numbers n such that tau(n+1) - tau(n) = 1).
%Y A227874 Cf. A230115 (numbers n such that tau(n+1) - tau(n) = 2).
%Y A227874 Cf. A230653 (numbers n such that tau(n+1) - tau(n) = 3).
%Y A227874 Cf. A230654 (numbers n such that tau(n+1) - tau(n) = 4).
%Y A227874 Cf. A228453 (numbers n such that tau(n+1) - tau(n) = 5).
%K A227874 nonn
%O A227874 1,1
%A A227874 _Jaroslav Krizek_, Nov 03 2013