A083681 Sum of divisors of semiprimes.

7, 12, 13, 18, 24, 24, 32, 36, 31, 42, 48, 54, 48, 60, 56, 72, 57, 72, 72, 80, 90, 96, 84, 96, 114, 96, 126, 108, 132, 120, 112, 128, 144, 120, 162, 152, 144, 180, 144, 133, 186, 168, 176, 160, 204, 192, 216, 168, 180, 222, 192, 240, 216, 192, 252, 183, 240, 270, 248

Offset: 1

Author

Shyam Sunder Gupta, Jun 15 2003

Keywords

• easy
• nonn

Comments

Contains all products of distinct terms of A008864 contributed by the squarefree semiprimes and all terms of A060800 contributed by the squared primes: 7 = A060800(1), 12 = A008864(1)*A008864(2), 13 = A060800(2), 18=A008864(1)*A008864(3) etc. - R. J. Mathar, Mar 15 2018

Examples

			a(2) = 12 because the sum of divisors of the 2nd semiprime, i.e. 6, is 1+2+3+6 = 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A001358, A006530, A008864, A020639, A060800.

Programs

Mathematica

DivisorSigma[1, Select[Range[200], PrimeOmega[#] == 2 &]] (* Amiram Eldar, Nov 24 2020 *)

Formula

a(n) = A000203(A001358(n)) = 1 + A020639(n) + A057427(A006530(n)-A020639(n))*A006530(n) + A020639(n)*A006530(n). - Reinhard Zumkeller, Jun 16 2003