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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A071090 A105221 A215339 * A058974 A369744 A326059
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

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)