A379898 - OEIS

%I #7 Jan 07 2025 10:09:48

%S 6,24,38,42,62,96,98,146,152,162,168,171,248,384,392,584,608,648,672,

%T 684,992,1026,1134,1202,1506,1536,1568,1674,2336,2432,2592,2646,2688,

%U 2736,3942,3968,4104,4214,4374,4536,4575,4617,4808,6024,6144,6272,6696,9344,9728

%N Integers k equal to the sum over A003415(t) mod t, for some steps, starting with t = k and then using the result to feed the next calculation.

%C Up to 10^7, the longest process takes place with 35966, 143864, 575456, 971082, 2301824, 3884328 and 9207296 which need 8 steps.

%e k = 146 (3 steps):

%e 146' mod 146 = 75;

%e 75' mod 75 = 55;

%e 55' mod 55 = 16 and 75 + 55 + 16 = 146.

%e k = 248 (4 steps):

%e 248' mod 248 = 132;

%e 132' mod 132 = 56;

%e 56' mod 56 = 36;

%e 36' mod 36 = 24 and 132 + 56 + 36 + 24 = 248.

%p with(numtheory): P:=proc(q) local a, b, n, v; v:=[]; for n from 1 to q do

%p a:=0; b:=n; while a<n do b:=(b*add(op(2,p)/op(1,p),p=ifactors(b)[2]) mod b);

%p if b=0 then break; else a:=a+b; fi; od; if a=n then v:=[op(v), n]; fi; od; op(v); end: P(10^4);

%Y Cf. A003415, A377001, A377002.

%K nonn,easy,new

%O 1,1

%A _Paolo P. Lava_, Jan 05 2025