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A375740
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Numbers k such that A007916(k+1) - A007916(k) = 1. In other words, the k-th non-perfect-power is 1 less than the next.
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4
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1, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77
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OFFSET
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1,2
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COMMENTS
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Positions in A007916 of numbers k such that k+1 is also a member.
Non-perfect-powers (A007916) are numbers with no proper integer roots.
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LINKS
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EXAMPLE
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The non-perfect-powers are 2, 3, 5, 6, 7, 10, 11, 12, 13, ... which increase by one after positions 1, 3, 4, 6, ...
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MATHEMATICA
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radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Join@@Position[Differences[Select[Range[100], radQ]], 1]
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PROG
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(Python)
from itertools import count, islice
from sympy import perfect_power
def A375740_gen(): # generator of terms
a, b = -1, 0
for n in count(2):
c = not perfect_power(n)
if c:
a += 1
if b&c:
yield a
b = c
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CROSSREFS
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Non-perfect-powers:
Non-prime-powers (exclusive):
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KEYWORD
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nonn,new
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AUTHOR
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STATUS
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approved
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