login
Numbers k such that there are 18 digits in k^2 and for each factor f of 18 (1,2,3,6,9) the sum of digit groupings of size f is a square.
1

%I #19 May 09 2021 07:53:32

%S 324344373,333306315,333321861,333359685,333361029,334363803,

%T 369396732,370397193,407380269,407381484,444475035,666636972,

%U 666695028,666701463,702667239,702671124,702736170,703667130,704741610

%N Numbers k such that there are 18 digits in k^2 and for each factor f of 18 (1,2,3,6,9) the sum of digit groupings of size f is a square.

%C This sequence is a subsequence of both A153745 and A061910.

%e 324344373^2 = 105199272296763129;

%e 1+0+5+1+9+9+2+7+2+2+9+6+7+6+3+1+2+9 = 81 = 9^2;

%e 10+51+99+27+22+96+76+31+29 = 441 = 21^2;

%e 105+199+272+296+763+129 = 1764 = 42^2;

%e 105199+272296+763129 = 1140624 = 1068^2;

%e 105199272+296763129 = 401962401 = 20049^2.

%Y Cf. A004159, A061910, A153745.

%K nonn,base,fini,full

%O 1,1

%A _Doug Bell_, Dec 31 2008