Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Jan 05 2017 21:01:26
%S 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,
%T 28,12,30,11,32,33,15,20,13,14,38,22,17,14,42,13,44,16,15,26,48,20,50,
%U 28,21,18,54,30,17,16,23,32,60,13,62,34,17,65,19,17,68,22,27,15,72,18,74
%N a(n) = A008475(n) + 1.
%C 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}.
%F a(n) = [Sum_(i=1,…, j) p_i^k_i] + 1 = A000203(n) - A178636(n).
%F 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.
%e 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.
%t f[n_] := 1 + Plus @@ Power @@@ FactorInteger@ n; f[1] = 1; Array[f, 60]
%o (PARI) a(n)=local(t); if(n<1, 0, t=factor(n); 1+sum(k=1, matsize(t)[1], t[k, 1]^t[k, 2])) /* _Anton Mosunov_, Jan 05 2017 */
%Y Cf. A008475, A023888.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Apr 04 2009
%E Edited by _N. J. A. Sloane_, Apr 07 2009