login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A375702
Length of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.
16
2, 3, 6, 8, 1, 4, 3, 12, 14, 16, 18, 20, 3, 2, 15, 24, 26, 19, 8, 17, 12, 32, 34, 18, 17, 38, 40, 42, 27, 16, 46, 48, 50, 52, 54, 56, 58, 60, 38, 23, 64, 66, 68, 70, 34, 37, 74, 76, 78, 80, 46, 35, 84, 86, 88, 22, 67, 70, 9, 11, 94, 96, 98, 100, 102, 39, 64
OFFSET
1,1
COMMENTS
Non-perfect-powers A007916 are numbers with no proper integer roots.
FORMULA
For n > 2 we have a(n) = A053289(n+1) - 1.
EXAMPLE
The list of all non-perfect-powers, split into runs, begins:
2 3
5 6 7
10 11 12 13 14 15
17 18 19 20 21 22 23 24
26
28 29 30 31
33 34 35
37 38 39 40 41 42 43 44 45 46 47 48
Row n has length a(n), first A375703, last A375704, sum A375705.
MATHEMATICA
radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Length/@Split[Select[Range[100], radQ], #1+1==#2&]//Most
CROSSREFS
For nonsquarefree numbers we have A053797, anti-runs A373409.
For squarefree numbers we have A120992, anti-runs A373127.
For nonprime numbers we have A176246, anti-runs A373403.
For prime-powers we have A373675, anti-runs A373576.
For non-prime-powers we have A373678, anti-runs A373679.
The anti-run version is A375736, sum A375737.
For runs of non-perfect-powers (A007916):
- length: A375702 (this).
- first: A375703
- last: A375704
- sum: A375705
A001597 lists perfect-powers, differences A053289.
A007916 lists non-perfect-powers, differences A375706.
A046933 counts composite numbers between primes.
Sequence in context: A291659 A302090 A088414 * A133441 A086254 A265297
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 27 2024
STATUS
approved