A373678 Sums of maximal runs of non-prime-powers.

1, 6, 10, 12, 29, 18, 63, 24, 26, 28, 30, 138, 117, 42, 135, 48, 153, 280, 60, 125, 131, 207, 72, 380, 80, 82, 430, 651, 297, 102, 315, 108, 333, 819, 369, 126, 259, 670, 138, 1296, 150, 770, 800, 495, 168, 513, 880, 180, 1674, 192, 585, 198, 2255, 2387, 675

Offset

1,2

Comments

We consider 1 to be a power of a prime and a non-prime-power, but not a prime-power.

A run of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by one.

Links

Table of n, a(n) for n=1..55.

Gus Wiseman, Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers.

Example

The maximal runs of non-powers of primes begin:
   1
   6
  10
  12
  14  15
  18
  20  21  22
  24
  26
  28
  30
  33  34  35  36
  38  39  40
  42
  44  45  46
  48
  50  51  52
  54  55  56  57  58
  60

Mathematica

Total/@Split[Select[Range[100], !PrimePowerQ[#]&], #1+1==#2&]//Most

Crossrefs

A000040 lists the primes, differences A001223.

A000961 lists all powers of primes (A246655 if not including 1).

A025528 counts prime-powers up to n.

A057820 gives first differences of consecutive prime-powers, gaps A093555.

A361102 lists all non-prime-powers (A024619 if not including 1).

See link for composite, prime, nonsquarefree, and squarefree runs.

Prime-power runs: A373675, min A373673, max A373674, length A174965.

Non-prime-power runs: A373678, min A373676, max A373677, length A110969.

Prime-power antiruns: A373576, min A120430, max A006549, length A373671.

Non-prime-power antiruns: A373679, min A373575, max A255346, length A373672.

Cf. A005117, A014963, A038664, A046933, A054265, A065855, A071148, A293697, A371201, A373400.

Sequence in context: A297620 A074924 A064166 * A107371 A340874 A213428

Adjacent sequences: A373675 A373676 A373677 * A373679 A373680 A373681

Keyword

nonn

Author

Gus Wiseman, Jun 16 2024

Status

approved