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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.
2
16, 64, 2744, 474552, 157529610000, 407165596771032, 1491025241529616, 173903694695292024, 661905356066769705912, 14918256451377811247508792, 19801061641727872277815512, 2718924063971620383558231552
OFFSET
1,1
COMMENTS
a(13) > 5*10^27.
EXAMPLE
Pairs b,c of consecutive terms of A076467
c-b b c = a(n)
8, 8, 16,
32, 32, 64,
343, 2401, 2744,
17576, 456976, 474552,
65610000, 157464000000, 157529610000,
11329982936, 407154266788096, 407165596771032,
26102469128, 1490999139060488, 1491025241529616,
315404039943, 173903379291252081, 173903694695292024,
152838610998696, 661905203228158707216, 661905356066769705912.
PROG
(PARI) \\ Uses M. F. Hasler's A076467_vec from A076467
rad(x) = vecprod(factor(x)[, 1]);
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]])))};
\\ Alternative program not using rad, more efficient
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]]))))};
a378166_7(10^18)
CROSSREFS
A378167 gives the corresponding values of c-b.
Sequence in context: A327496 A330824 A189806 * A222748 A283271 A031446
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Nov 20 2024
STATUS
approved