A307861 - OEIS

%I #39 May 08 2019 17:51:11

%S 1,11,121,1111,12221,134431,1234321,1478741,1600951,17610461,

%T 161696051,193715071,1634570971

%N Numbers that set records on longest chains of "Chained Divisors" of A306661 and A307858.

%C Here are the divisor chains:

%C Length---m----------Divisors

%C   1      1            {1}

%C   2      11           {1,11}

%C   3      121          {1,11,121}

%C   4      1111         {1,11,101,1111}

%C   6      12221        {1,11,101,121,1111,12221}

%C   8      134431       {1,11,101,121,1111,1331,12221,134431}

%C   9      1234321      {1,11,101,121,1111,10201,12221,112211,1234321}

%C   10     1478741      {1,11,101,121,1111,1331,12221,14641,134431,1478741}

%C The longest chain known is of number 1634570971 of length 24.

%C Under the assumption that all divisors begin and end with 1, the next terms are 19565222171, 153203879191, 165091668071, 197783087491, and 1685242671101, with 30, 32, 36, 40, and 48 divisors, respectively. - _Charlie Neder_, May 08 2019

%o (PARI) { mx=0; for (n=1, oo, if (#(d=divisors(n))>mx, ok=1; d=apply(digits,d); for (i=1, #d-1, if (d[i][#d[i]]!=d[i+1][1], ok=0; break)); if (ok,

%o print1 (n ", "); mx=#d))) } \\ _Rémy Sigrist_, May 06 2019

%Y Cf. A307858, A306661.

%K nonn,base,more

%O 1,2

%A _Giorgos Kalogeropoulos_, May 05 2019

%E a(11)-a(13) from _Rémy Sigrist_, May 06 2019