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Record gaps between nonprime prime powers.
3

%I #13 Jul 27 2024 13:55:12

%S 3,4,7,9,17,40,41,74,151,307,312,408,424,912,1032,1217,1872,2518,3713,

%T 4920,5208,8400,8520,8892,9297,12840,16008,21840,24360,35880,38808,

%U 80760,102168,129480,167160,183960,201072,258720,290760,301242,358848,375468,415920

%N Record gaps between nonprime prime powers.

%H Donovan Johnson, <a href="/A167186/b167186.txt">Table of n, a(n) for n = 1..200</a>

%e 17 is in the sequence since A025475(9) - A025475(8) = 49 - 32 = 17, and no previous gap is larger.

%e A025475(10) - A025475(9) = 64 - 49 = 15, but the previous gap is larger, so 15 is not in the sequence.

%t Join[{3},DeleteDuplicates[Differences[Select[Range[10^6],PrimePowerQ[#] && !PrimeQ[ #]&]], GreaterEqual]] (* _Harvey P. Dale_, Feb 28 2023 *)

%o (PARI) isA025475(n) = (omega(n) == 1 & !isprime(n)) || (n == 1)

%o d_max=0;n_prev=1;for(n=2,32e6,if(isA025475(n),d=n-n_prev;n_prev=n;if(d>d_max,print(d);d_max=d)))

%Y List of nonprime prime powers: A025475.

%Y Gaps between nonprime prime powers: A053707.

%Y Record gaps between prime powers including primes: A121492.

%K nonn

%O 1,1

%A _Michael B. Porter_, Oct 29 2009, Oct 31 2009, Nov 03 2009