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A272714
Numbers n such that both n and n+1 are Achilles numbers (A052486).
0
5425069447, 11968683934831, 28821995554247, 48689748233307
OFFSET
1,1
COMMENTS
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?
EXAMPLE
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.
PROG
(PARI) is(n) = vecmin(factor(n)[, 2]) > 1 && vecmin(factor(n+1)[, 2]) > 1 && !ispower(n) && !ispower(n+1)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Felix Fröhlich, May 12 2016
STATUS
approved