This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378166 #16 Nov 29 2024 05:11:38
%S A378166 16,64,2744,474552,157529610000,407165596771032,1491025241529616,
%T A378166 173903694695292024,661905356066769705912,14918256451377811247508792,
%U A378166 19801061641727872277815512,2718924063971620383558231552
%N A378166 Terms c = A076467(k) such that the distinct prime factors of b = A076467(k-1) and of c-b are subsets of the prime factors of c, i.e., rad(c)/rad((c-b)*b*c) = 1.
%C A378166 a(13) > 5*10^27.
%e A378166 Pairs b,c of consecutive terms of A076467
%e A378166 A378167
%e A378166 c-b b c = a(n)
%e A378166 8, 8, 16,
%e A378166 32, 32, 64,
%e A378166 343, 2401, 2744,
%e A378166 17576, 456976, 474552,
%e A378166 65610000, 157464000000, 157529610000,
%e A378166 11329982936, 407154266788096, 407165596771032,
%e A378166 26102469128, 1490999139060488, 1491025241529616,
%e A378166 315404039943, 173903379291252081, 173903694695292024,
%e A378166 152838610998696, 661905203228158707216, 661905356066769705912.
%o A378166 (PARI) \\ Uses _M. F. Hasler_'s A076467_vec from A076467
%o A378166 rad(x) = vecprod(factor(x)[,1]);
%o A378166 a378166_7(upto) = {my(W=A076467_vec(upto)); for(k=2, #W, my(d=W[k]-W[k-1], q=rad(W[k])/rad(W[k]*W[k-1]*d)); if(q==1, print([d, W[k-1], W[k]])))};
%o A378166 \\ Alternative program not using rad, more efficient
%o A378166 a378166_7(upto) = {my(W=A076467_vec(upto)); for(k=2, #W, my(C=Set(factor(W[k])[,1]), d=W[k]-W[k-1]); if(#setminus(Set(factor(d)[,1]), C)>0, , if(#setminus(Set(factor(W[k-1])[,1]), C)==0, print([d, W[k-1], W[k]]))))};
%o A378166 a378166_7(10^18)
%Y A378166 A378167 gives the corresponding values of c-b.
%Y A378166 Cf. A007947 (rad), A076467, A378164, A378165.
%K A378166 nonn,hard,more
%O A378166 1,1
%A A378166 _Hugo Pfoertner_, Nov 20 2024