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.

4, 16, 64, 128, 6912, 24576, 16384, 786432, 524288, 50096498540544, 3764488749034090683017723904, 167633515663893895281332936606596215078912

Offset: 1

Author

Farideh Firoozbakht, Jul 01 2009, Jul 08 2009

Keywords

• base
• nonn

Comments

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

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

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

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

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

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

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

& {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.

Crossrefs

Cf. A097655.