A098383 Define a function f on the positive integers by: if n is 1 or composite, stop; but if n = prime(k) then f(n) = k; a(n) = sum of terms in trajectory of n under repeated application of f.

1, 3, 6, 4, 11, 6, 11, 8, 9, 10, 22, 12, 19, 14, 15, 16, 28, 18, 27, 20, 21, 22, 32, 24, 25, 26, 27, 28, 39, 30, 53, 32, 33, 34, 35, 36, 49, 38, 39, 40, 60, 42, 57, 44, 45, 46, 62, 48, 49, 50, 51, 52, 69, 54, 55, 56, 57, 58, 87, 60, 79, 62, 63, 64, 65, 66, 94, 68, 69, 70, 91, 72

Offset

1,2

Comments

Sum of the terms in the prime index chain for n (cf. A049076).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. Fernandez, An order of primeness, F(p)

N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Example

a(2) = 3 because 2 is the first prime, therefore 2 + 1 = 3. a(3) = 6 because 3 is the second prime and two is the first prime, therefore 3 + 2 + 1 = 6. a(4) = 4 because 4 is composite. a(5) = 11 because five is the third prime, three is the second prime and two is the first prime, which gives us 5 + 3 + 2 + 1 = 11 and so on.

Maple

a:= n-> n + `if`(isprime(n), a(numtheory[pi](n)), 0):
seq (a(n), n=1..80);  # Alois P. Heinz, Jul 16 2012

Mathematica

Table[s=n; p=n; While[PrimeQ[p], p=PrimePi[p]; s=s+p]; s, {n, 1000}] (T. D. Noe)

Crossrefs

Cf. A007097, A057450, A057451, A049076.

Sequence in context: A122634 A169846 A169854 * A328637 A162523 A292681

Adjacent sequences: A098380 A098381 A098382 * A098384 A098385 A098386

Keyword

easy,nonn

Author

Andrew S. Plewe, Oct 26 2004

Extensions

More terms from Ray Chandler, Nov 04 2004

Status

approved