login
Numbers n such that d(n-1) = d(n+1) = 4, where d(k) is the number of divisors of k (A000005).
3

%I #12 Feb 10 2019 01:21:45

%S 7,9,34,56,86,92,94,124,142,144,160,184,186,202,204,214,216,218,220,

%T 236,248,266,300,302,304,320,322,328,340,342,392,394,412,414,416,446,

%U 452,470,472,516,518,534,536,544,552,580,582,590,634,668,670,680,686

%N Numbers n such that d(n-1) = d(n+1) = 4, where d(k) is the number of divisors of k (A000005).

%C Numbers n such that n-1 and n+1 are both multiplicatively perfect numbers A007422.

%H Nathaniel Johnston, <a href="/A189974/b189974.txt">Table of n, a(n) for n = 1..10000</a>

%p with(numtheory): A189974 := proc(n) option remember: local k: if(n=1)then return 7:else k:=procname(n-1)+1: do if(tau(k-1)=4 and tau(k+1)=4)then return k: fi: k:=k+1: od: fi: end: seq(A189974(n),n=1..60); # _Nathaniel Johnston_, May 04 2011

%t Select[Range[2, 754], DivisorSigma[0, # - 1] == DivisorSigma[0, # + 1] == 4 &]

%Y Cf. A000005, A007422.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, May 03 2011