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A023888
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Sum of prime power divisors of n (1 included).
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1
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1, 3, 4, 7, 6, 6, 8, 15, 13, 8, 12, 10, 14, 10, 9, 31, 18, 15, 20, 12, 11, 14, 24, 18, 31, 16, 40, 14, 30, 11, 32, 63, 15, 20, 13, 19, 38, 22, 17, 20, 42, 13, 44, 18, 18, 26, 48, 34, 57, 33, 21, 20, 54, 42, 17, 22, 23, 32, 60, 15, 62, 34, 20, 127, 19, 17, 68, 24, 27
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = A000203(n) - A035321(n) = A023889(n) + 1.
a(1) = 1, a(p) = p+1, a(pq) = p+q+1, a(pq...z) = (p+q+...+z) + 1, a(p^k) = (p^(k+1)-1) / (p-1), for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.
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EXAMPLE
| For n = 12, set of such divisors is {1, 2, 3, 4}; a(12) = 1+2+3+4 = 10. From
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MATHEMATICA
| Array[ Plus @@ (Select[ Divisors[ # ], (Length[ FactorInteger[ # ] ]<=1)& ])&, 70 ]
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PROG
| (PARI) for(n=1, 100, s=1; fordiv(n, d, if((ispower(d, , &z)&&isprime(z)) || isprime(d), s+=d)); print1(s, ", "))
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CROSSREFS
| Sequence in context: A190998 A067342 A105827 * A117553 A168275 A120224
Adjacent sequences: A023885 A023886 A023887 * A023889 A023890 A023891
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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