A378166 - OEIS

%I #16 Nov 29 2024 05:11:38

%S 16,64,2744,474552,157529610000,407165596771032,1491025241529616,

%T 173903694695292024,661905356066769705912,14918256451377811247508792,

%U 19801061641727872277815512,2718924063971620383558231552

%N 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 a(13) > 5*10^27.

%e                       Pairs b,c of consecutive terms of A076467

%e           A378167

%e               c-b                      b               c = a(n)

%e                 8,                     8,                    16,

%e                32,                    32,                    64,

%e               343,                  2401,                  2744,

%e             17576,                456976,                474552,

%e          65610000,          157464000000,          157529610000,

%e       11329982936,       407154266788096,       407165596771032,

%e       26102469128,      1490999139060488,      1491025241529616,

%e      315404039943,    173903379291252081,    173903694695292024,

%e   152838610998696, 661905203228158707216, 661905356066769705912.

%o (PARI) \\ Uses _M. F. Hasler_'s A076467_vec from A076467

%o rad(x) = vecprod(factor(x)[,1]);

%o 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 \\ Alternative program not using rad, more efficient

%o 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_7(10^18)

%Y A378167 gives the corresponding values of c-b.

%Y Cf. A007947 (rad), A076467, A378164, A378165.

%K nonn,hard,more

%O 1,1

%A _Hugo Pfoertner_, Nov 20 2024