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A062069
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a(n) = sigma(d(n)), where d(k) is the number of divisors function (A000005) and sigma(k) is the sum of divisor function (A000203).
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18
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1, 3, 3, 4, 3, 7, 3, 7, 4, 7, 3, 12, 3, 7, 7, 6, 3, 12, 3, 12, 7, 7, 3, 15, 4, 7, 7, 12, 3, 15, 3, 12, 7, 7, 7, 13, 3, 7, 7, 15, 3, 15, 3, 12, 12, 7, 3, 18, 4, 12, 7, 12, 3, 15, 7, 15, 7, 7, 3, 28, 3, 7, 12, 8, 7, 15, 3, 12, 7, 15, 3, 28, 3, 7, 12, 12, 7, 15, 3, 18, 6, 7, 3, 28, 7, 7, 7, 15, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(1) = 1, a(p) = 3 for p = primes (A000040), a(pq) = 7 for pq = product of two distinct primes (A006881), a(pq...z) = 2^(k+1)-1 = A000225(k+1) for pq...z = product of k (k > 2) distinct primes p,q,...,z (A120944), a(p^k) = sigma(k+1) = A000203(k+1) for p^k = prime powers (A000961(n) for n > 1). Sequence {1,3,4,12} is finite sequence of numbers n such that sigma(tau(n)) = n. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jul 16 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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EXAMPLE
| sigma(d(12)) = sigma(6) = 12.
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MAPLE
| A062069:= (n-> numtheory[sigma](numtheory[tau](n))):
seq (A062069(n), n=1..40); # - Jani Melik, Jan 25 2011
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MATHEMATICA
| Table[DivisorSigma[1, DivisorSigma[0, n]], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *)
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PROG
| (PARI) v=[]; for(n=1, 150, v=concat(v, sigma(numdiv(n)))); v
(PARI) { for (n=1, 1000, write("b062069.txt", n, " ", sigma(numdiv(n))) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 31 2009]
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CROSSREFS
| Cf. A062068.
Sequence in context: A163523 A151664 A083503 * A163375 A027011 A174280
Adjacent sequences: A062066 A062067 A062068 * A062070 A062071 A062072
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 13 2001
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EXTENSIONS
| More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jun 19 2001
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