cp's OEIS Frontend

A158988 Numbers n such that n=phi(d_1!!)*phi(d_2!!)*...*phi(d_k!!) where d_1...d_k is the decimal expansion of n.

%I A158988 #5 Feb 04 2025 05:40:59
%S A158988 4,16,64,128,6912,24576,16384,786432,524288,50096498540544,
%T A158988 3764488749034090683017723904,
%U A158988 167633515663893895281332936606596215078912
%N A158988 Numbers n such that n=phi(d_1!!)*phi(d_2!!)*...*phi(d_k!!) where d_1...d_k is the decimal expansion of n.
%C A158988 All terms are of the form 2^i*3^j where i and j are nonnegative integers.
%C A158988 So corresponding to each term a(n) of the sequence there exists a unique pair
%C A158988 (i(n),j(n)) such that a(n)=2^i(n)*3^j(n). {n,(i(n),j(n))} for n=1, 2, ...,
%C A158988 24 are: {1,(2,0)},{2,(4,0)},{3,(6,0)},{4,(7,0)},{5,(8,3)},{6,(14,0)},{7,(13,1)},
%C A158988 {8,(19,0)},{9,(18,1)},{10,(36,6)},{11,(71,13)},{12,(110,17)},{13,(206,24)},
%C A158988 {14,(200,30)},{15,(679,118)},{16,(679,123)},{17,(766,136)},{18,(868,158)},
%C A158988 {19,(1032,160)},{20,(1207,199)},{21,(1258,171)},{22,(1257,209)},{23,(1326,199)},
%C A158988 & {24,(3291,531)}. So for example a(10)=2^36*3^6=50096498540544 and a(24), the largest known term of the sequence, is 2^3291*3^531.
%Y A158988 Cf. A097655.
%K A158988 base,nonn
%O A158988 1,1
%A A158988 _Farideh Firoozbakht_, Jul 01 2009, Jul 08 2009