A061376 a(n) = f(n) + f(f(n)) where f(n) = 0 if n <= 1 or a prime, otherwise f(n) = sum of distinct primes dividing n.

0, 0, 0, 2, 0, 5, 0, 2, 3, 7, 0, 5, 0, 12, 10, 2, 0, 5, 0, 7, 17, 13, 0, 5, 5, 23, 3, 12, 0, 17, 0, 2, 23, 19, 17, 5, 0, 31, 18, 7, 0, 17, 0, 13, 10, 30, 0, 5, 7, 7, 27, 23, 0, 5, 18, 12, 35, 31, 0, 17, 0, 47, 17, 2, 23, 18, 0, 19, 41, 23, 0, 5, 0, 55, 10, 31, 23, 23, 0, 7

Offset

1,4

Comments

Note that this sequence differs from A058974 at n = 26, 33, 38, 52, 62, 69, 70, 74, 76, 86, 99, etc.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Example

a(14) = 12 because f(14) = 2+7 = 9 and f(9) = 3 and 9+3 = 12.
From David A. Corneth, Oct 30 2017: (Start)
To find the first 20 terms, make a list called res with offset 1 of size 20. For each prime p, increase multiples p * k of p with k > 1 by p. This gives
[0, 0, 0, 2, 0, 5, 0, 2, 3, 7, 0, 5, 0, 9, 8, 2, 0, 5, 0, 7].
Then, from the last element to the first, increase that element with the value of that element. For example, res[20] is 7, so we increase res[20] with the value of res[7]. res[7] is 0, so a(20) = 7 + 0 = 7. Repeat for all terms until 1. (End)

Mathematica

f[n_Integer] := If[n == 1 || PrimeQ[n], 0, Plus@@First[ Transpose[ FactorInteger[n] ] ] ]; Table[ f[n] + f[f[n]], {n, 1, 80} ]

Prog

(PARI)
A008472(n) = vecsum(factor(n)[, 1]); \\ M. F. Hasler, Jul 18 2015
f(n) = if((n<=1)||isprime(n), 0, A008472(n));
A061376(n) = f(n) + f(f(n)); \\ Antti Karttunen, Oct 30 2017
(PARI) first(n) = {my(res = vector(n)); forprime(p = 2, n, for(k = 2, n \ p, res[k*p] += p)); forstep(i = n, 1, -1, if(res[i]!=0, res[i] += res[res[i]])); res} \\ David A. Corneth, Oct 30 2017

Crossrefs

Cf. A008472, A058974.

Sequence in context: A071090 A105221 A215339 * A058974 A369744 A326059

Adjacent sequences: A061373 A061374 A061375 * A061377 A061378 A061379

Keyword

nonn,easy

Author

Robert G. Wilson v, Jun 08 2001

Extensions

Minor correction to the formula from Antti Karttunen, Oct 30 2017

Status

approved