

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
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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 fractallike 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



