OFFSET
1,1
EXAMPLE
The first number line below shows the perfect-powers. The second shows the primes. The third is a(n).
-1-----4-------8-9------------16----------------25--27--------32------36----
===2=3===5===7======11==13======17==19======23==========29==31==========37==
4 8 16 25 32
The terms together with their prime indices begin:
4: {1,1}
8: {1,1,1}
16: {1,1,1,1}
25: {3,3}
32: {1,1,1,1,1}
49: {4,4}
64: {1,1,1,1,1,1}
81: {2,2,2,2}
100: {1,1,3,3}
121: {5,5}
128: {1,1,1,1,1,1,1}
144: {1,1,1,1,2,2}
169: {6,6}
196: {1,1,4,4}
216: {1,1,1,2,2,2}
225: {2,2,3,3}
243: {2,2,2,2,2}
256: {1,1,1,1,1,1,1,1}
MATHEMATICA
radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Union[Table[NestWhile[#+1&, Prime[n], radQ[#]&], {n, 100}]]
CROSSREFS
A version for prime-powers (but starting with prime(k) + 1) is A345531.
A069623 counts perfect-powers <= n.
A076411 counts perfect-powers < n.
A131605 lists perfect-powers that are not prime-powers.
A377432 counts perfect-powers between primes, zeros A377436, positive A377283, postpositive A377466.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 21 2024
STATUS
approved