| Smooth Power Duos: Search for consecutive numbers a(n)-1 and a(n) such that
the largest prime factor of a(n)-1 raised to the power n remains <= a(n)-1 and such that
the largest prime factor of a(n) raised to the power n remains <= a(n):
( A006530(a(n)))^n <= a(n) and (A006530(a(n)-1))^n <= a(n)-1.
The prime factorization for the a(n) and a(n)-1 are:
n=1: 3=3, 2=2. n=2: 9=3^2, 8= 2^3. n=3 or 4: 2401=7^4, 2400=2^5*3*5^2.
n=5: 5909761 = 11^2*13^2*17^2, 5909760 = 2^8*3^5*5*19.
n=6: 1611308700 = 2^2*3^6*5^2*23*31^2, 1611308699 = 7^4*11*13^2*19^2 .
n=7: 421138799640 = 2^3*3^5*5*13^4*37*41, 421138799639 = 17*19*23^2*31*43^3 .
n=8: 2286831727304145 = 3^15*5*7^3*19*67*73, 2286831727304144 = 2^4*17*23^2*37*41^2*59*61*71 .
n=9: 3948741978036988496 = 2^4*7^5*13*23*43*59^3*67*83, 3948741978036988495 = 5*11*17*31*97^2*101*103*109*113^2 .
Note: All numbers through 2^62 have been searched
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