A269304 a(n) = n + n/gpf(n) + 1, where gpf(n) is the greatest prime factor of n or 1 if n = 1.

3, 4, 5, 7, 7, 9, 9, 13, 13, 13, 13, 17, 15, 17, 19, 25, 19, 25, 21, 25, 25, 25, 25, 33, 31, 29, 37, 33, 31, 37, 33, 49, 37, 37, 41, 49, 39, 41, 43, 49, 43, 49, 45, 49, 55, 49, 49, 65, 57, 61, 55, 57, 55, 73, 61, 65, 61, 61, 61, 73, 63, 65, 73, 97, 71, 73, 69

Offset

1,1

Comments

a(n) is odd except when n=2.

Initially, a(n) is frequently a square or a prime.

It is conjectured that any two sequences generated with a(n)=a(n-1)+a(n-1)/gpf(a(n-1))+1 and any initial value >=1 will have a finite number of non-shared terms and an infinite number of shared terms after one initial shared term (see A270807). Example: For a(1)=314, the sequence generated is 314, 317, 319, 331, 333, 343, 393, 397, 399, 421, 423, 433, ...; for a(1)=97, the sequence generated is 97, 99, 109, 111, 115, 121, 133, 141, 145, 151, 153, 163, 165, 181, 183, 187, 199, 201, 205, 211, 213, 217, 225, 271, 273, 295, 301, 309, 313, 315, 361, 381, 385, 421, 423, 433, ...; these sequences have respectively 9 and 33 terms not shared with the other until both reach 421; the following terms of both sequences are identical.

Links

Cody M. Haderlie, Table of n, a(n) for n = 1..10000

Formula

a(n) = n + n/A006530(n) + 1.

a(n) = n + A052126(n) + 1.

a(p) = p+2 for p prime.

Example

For n=18765, a(n)=18901.
For n=196, a(n)=225 (225 is a square).
For n=103156, a(n)=105673 (105673 is prime).

Mathematica

Table[n+n/FactorInteger[n][[-1, 1]]+1, {n, 100}]

Prog

(PARI) gpf(n)=if(n>1, my(f=factor(n)[, 1]); f[#f], 1)
a(n)=n + n/gpf(n) + 1 \\ Charles R Greathouse IV, Feb 22 2016

Crossrefs

Cf. A006530, A052126, A270807.

Sequence in context: A049465 A196122 A247140 * A071054 A379337 A231346

Adjacent sequences: A269301 A269302 A269303 * A269305 A269306 A269307

Keyword

nonn,easy,hear

Author

Cody M. Haderlie, Feb 22 2016

Status

approved