A049087 Ceiling of mean distance between successive distinct prime divisors of n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 5, 2, 0, 0, 1, 0, 3, 4, 9, 0, 1, 0, 11, 0, 5, 0, 2, 0, 0, 8, 15, 2, 1, 0, 17, 10, 3, 0, 3, 0, 9, 2, 21, 0, 1, 0, 3, 14, 11, 0, 1, 6, 5, 16, 27, 0, 2, 0, 29, 4, 0, 8, 5, 0, 15, 20, 3, 0, 1, 0, 35, 2, 17, 4, 6, 0, 3, 0, 39, 0, 3, 12, 41, 26, 9, 0, 2, 6, 21, 28, 45

Offset

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

a(105)=2: prime divisors of 105 are 3,5,7; distance between successive pairs: 5-3=2 and 7-5=2; mean of 2 and 2 is 2.
If n=30 the mean is 1.5 and rounding up, a(30)=2.

Mathematica

Table[Ceiling[Mean[Differences[FactorInteger[n][[All, 1]]]/.{}->{0, 0}]], {n, 100}] (* Harvey P. Dale, Jun 26 2021 *)

Prog

(PARI) A049087(n) = if(1>=omega(n), 0, my(ps = factor(n)[, 1], s = 0); for(i=2, #ps, s += (ps[i]-ps[i-1])); ceil(s/(#ps-1))); \\ Antti Karttunen, Sep 07 2018

Crossrefs

Cf. also A178921.

Sequence in context: A331332 A300228 A100573 * A178921 A046665 A100574

Adjacent sequences: A049084 A049085 A049086 * A049088 A049089 A049090

Keyword

easy,nonn

Author

Enoch Haga

Status

approved