A135323 a(1)=1, a(n) = Sum_{p=prime, p|n} a(n/p)*p.

1, 2, 3, 4, 5, 12, 7, 8, 9, 20, 11, 36, 13, 28, 30, 16, 17, 54, 19, 60, 42, 44, 23, 96, 25, 52, 27, 84, 29, 180, 31, 32, 66, 68, 70, 216, 37, 76, 78, 160, 41, 252, 43, 132, 135, 92, 47, 240, 49, 150, 102, 156, 53, 216, 110, 224, 114, 116, 59, 720, 61, 124, 189, 64, 130, 396

Offset

1,2

Comments

If p^k is a power of a prime, then a(p^k) = p^k.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(n) = n * A008480(n). - Ivan Neretin, May 29 2016

Example

The primes that divide 12 are 2 and 3. So a(12) = a(12/2)*2 + a(12/3)*3 = 12*2 + 4*3 = 36.

Mathematica

a = {1}; For[n = 2, n < 100, n++, b = Select[Divisors[n], PrimeQ[ # ] &]; AppendTo[a, Sum[a[[n/b[[j]]]]*b[[j]], {j, 1, Length[b]}]]]; a (* Stefan Steinerberger, Dec 07 2007 *)
Fold[Append[#1, Plus @@ ((p = Select[Divisors[#2], PrimeQ])*#1[[#2/p]])] &, {1}, Range[2, 66]] (* Ivan Neretin, May 29 2016 *)

Crossrefs

Sequence in context: A328260 A229347 A367167 * A052106 A064446 A352257

Adjacent sequences: A135320 A135321 A135322 * A135324 A135325 A135326

Keyword

nonn

Author

Leroy Quet, Dec 06 2007

Extensions

More terms from Stefan Steinerberger, Dec 07 2007

Status

approved