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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.
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%I #5 Feb 04 2025 05:40:59

%S 4,16,64,128,6912,24576,16384,786432,524288,50096498540544,

%T 3764488749034090683017723904,

%U 167633515663893895281332936606596215078912

%N 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 All terms are of the form 2^i*3^j where i and j are nonnegative integers.

%C So corresponding to each term a(n) of the sequence there exists a unique pair

%C (i(n),j(n)) such that a(n)=2^i(n)*3^j(n). {n,(i(n),j(n))} for n=1, 2, ...,

%C 24 are: {1,(2,0)},{2,(4,0)},{3,(6,0)},{4,(7,0)},{5,(8,3)},{6,(14,0)},{7,(13,1)},

%C {8,(19,0)},{9,(18,1)},{10,(36,6)},{11,(71,13)},{12,(110,17)},{13,(206,24)},

%C {14,(200,30)},{15,(679,118)},{16,(679,123)},{17,(766,136)},{18,(868,158)},

%C {19,(1032,160)},{20,(1207,199)},{21,(1258,171)},{22,(1257,209)},{23,(1326,199)},

%C & {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 Cf. A097655.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, Jul 01 2009, Jul 08 2009