1,1

Any term of the sequence is also a term of A227297, but the converse is not always true. The smallest term of A227297 where the converse fails is A227297(1) = 12167. Do any other such numbers exist?

Wikipedia, Achilles number

5425069447 = 7^3 * 41^2 * 97^2 and 5425069448 = 2^3 * 26041^2. Since every prime factor of 5425069447 and 5425069448 is repeated, both numbers are Achilles numbers (A052486) and since the two numbers differ by 1, i.e., the value of A247246 at the index of 5425069447 in A052486 is 1, 5425069447 is a term of the sequence.

(PARI) is(n) = vecmin(factor(n)[, 2]) > 1 && vecmin(factor(n+1)[, 2]) > 1 && !ispower(n) && !ispower(n+1)

Cf. A052486, A227297, A247246.

Sequence in context: A115414 A358412 A112430 * A389009 A376255 A213254

Adjacent sequences: A272711 A272712 A272713 * A272715 A272716 A272717

nonn,hard,more

Felix Fröhlich, May 12 2016

approved