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1, 3, 4, 5, 6, 6, 8, 9, 10, 8, 12, 8, 14, 10, 9, 17, 18, 12, 20, 10, 11, 14, 24, 12, 26, 16, 28, 12, 30, 11, 32, 33, 15, 20, 13, 14, 38, 22, 17, 14, 42, 13, 44, 16, 15, 26, 48, 20, 50, 28, 21, 18, 54, 30, 17, 16, 23, 32, 60, 13, 62, 34, 17, 65, 19, 17, 68, 22, 27, 15, 72, 18, 74
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If n = Product (p_i^k_i) for i = 1, …, j then a(n) is sum of divisor d from set of divisors{1, p_1^k_1, p_2^k_2, …, p_j^k_j}.
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FORMULA
| a(n) = [Sum_(i=1,…, j) p_i^k_i] + 1 = A000203(n) - A178636(n).
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, 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 divisors {1, p_1^k_1, p_2^k_2, …, p_j^k_j}: {1, 3, 4}. a(12) = 1+3+4=8.
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MATHEMATICA
| f[n_] := 1 + Plus @@ Power @@@ FactorInteger@ n; f[1] = 1; Array[f, 60]
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CROSSREFS
| Cf.: A008475.
Sequence in context: A198466 A159624 A036288 * A049267 A111608 A126800
Adjacent sequences: A159074 A159075 A159076 * A159078 A159079 A159080
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KEYWORD
| nonn
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AUTHOR
| Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Apr 04 2009
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EXTENSIONS
| Edited by N. J. A. Sloane, Apr 07 2009
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