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A375714
Positions of non-successions of consecutive non-perfect-powers. Numbers k such that the k-th non-perfect-power is at least two fewer than the next.
16
2, 5, 11, 19, 20, 24, 27, 39, 53, 69, 87, 107, 110, 112, 127, 151, 177, 196, 204, 221, 233, 265, 299, 317, 334, 372, 412, 454, 481, 497, 543, 591, 641, 693, 747, 803, 861, 921, 959, 982, 1046, 1112, 1180, 1250, 1284, 1321, 1395, 1471, 1549, 1629, 1675, 1710
OFFSET
1,1
COMMENTS
Non-perfect-powers (A007916) are numbers with no proper integer roots.
FORMULA
A007916(a(n)+1) - A007916(a(n)) > 1.
EXAMPLE
The initial non-perfect-powers are 2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, which increase by more than one after term 2, term 5, term 11, etc.
MATHEMATICA
radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
ce=Select[Range[100], radQ];
Select[Range[Length[ce]-1], !ce[[#+1]]==ce[[#]]+1&]
PROG
(Python)
from itertools import count, islice
from sympy import perfect_power
def A375714_gen(): # generator of terms
a, b = -1, 0
for n in count(1):
c = not perfect_power(n)
if c:
a += 1
if b&(c^1):
yield a
b = c
A375714_list = list(islice(A375714_gen(), 52)) # Chai Wah Wu, Sep 11 2024
CROSSREFS
First differences are A375702.
Positions of terms > 1 in A375706 (differences of A007916).
The complement for non-prime-powers is A375713, differences A373672.
The complement is A375740.
The version for non-prime-powers is A375928, differences A110969.
Prime-powers inclusive:
- terms: A000961
- differences: A057820
Non-prime-powers inclusive:
- terms: A361102
- differences: A375708
Sequence in context: A132455 A132459 A308517 * A101057 A045362 A157978
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 10 2024
STATUS
approved