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 A062069 a(n) = sigma(d(n)), where d(k) is the number of divisors function (A000005) and sigma(k) is the sum of divisors function (A000203). 21
 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; text; internal format)
 OFFSET 1,2 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. [Jaroslav Krizek, Jul 16 2009] For semiprime n, a(n) is either 4 or 7. Also a(n) = d(n) + omega(n) + mu(n), the sum of three core sequences A000005, A001221 and A008683. When n is semiprime, a(n) is completely defined by the Mobius function as: a(n) = 4 + 3*mu(n). a(n) also has the fractal-like identities a(d(n)) = d(n) and a(n) = sigma(a(d(n))). - Wesley Ivan Hurt, Sep 02 2013 If n is a triprime (A014612), d(n) is 4, 6, or 8 and a(n) = sigma(d(n)) is 7, 12, or 15 respectively. Then a(n) = -d(n)^2/4 + 5*d(n) - 9. - Wesley Ivan Hurt, Sep 08 2013 LINKS Harry J. Smith, Table of n, a(n) for n=1,...,1000 FORMULA a(n) = A000203(A000005(n)). - Wesley Ivan Hurt, Sep 09 2013 EXAMPLE sigma(d(12)) = sigma(6) = 12. MAPLE A062069:= (n-> numtheory[sigma](numtheory[tau](n))): seq (A062069(n), n=1..40); # Jani Melik, Jan 25 2011 MATHEMATICA Table[DivisorSigma[1, DivisorSigma[0, n]], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *) 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))) ) } \\ Harry J. Smith, Jul 31 2009 CROSSREFS Cf. A000005, A000203, A001221, A008683, A062068. Sequence in context: A163523 A151664 A083503 * A163375 A027011 A267048 Adjacent sequences:  A062066 A062067 A062068 * A062070 A062071 A062072 KEYWORD nonn AUTHOR Amarnath Murthy, Jun 13 2001 EXTENSIONS More terms from Jason Earls, Jun 19 2001 STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)