A167186 Record gaps between nonprime prime powers.

3, 4, 7, 9, 17, 40, 41, 74, 151, 307, 312, 408, 424, 912, 1032, 1217, 1872, 2518, 3713, 4920, 5208, 8400, 8520, 8892, 9297, 12840, 16008, 21840, 24360, 35880, 38808, 80760, 102168, 129480, 167160, 183960, 201072, 258720, 290760, 301242, 358848, 375468, 415920

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..200

Example

17 is in the sequence since A025475(9) - A025475(8) = 49 - 32 = 17, and no previous gap is larger.
A025475(10) - A025475(9) = 64 - 49 = 15, but the previous gap is larger, so 15 is not in the sequence.

Mathematica

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

Prog

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

Crossrefs

List of nonprime prime powers: A025475.

Gaps between nonprime prime powers: A053707.

Record gaps between prime powers including primes: A121492.

Sequence in context: A364684 A048849 A076211 * A221212 A218278 A101062

Adjacent sequences: A167183 A167184 A167185 * A167187 A167188 A167189

Keyword

nonn

Author

Michael B. Porter, Oct 29 2009, Oct 31 2009, Nov 03 2009

Status

approved