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A086718 Convolution of sequence of primes with sequence sigma(n).

%I A086718 #20 Dec 21 2021 21:11:55
%S A086718 2,9,22,48,85,151,231,355,500,709,937,1267,1617,2069,2575,3193,3860,
%T A086718 4686,5549,6593,7725,8985,10337,11961,13591,15464,17498,19714,22036,
%U A086718 24690,27378,30382,33603,37023,40597,44733,48720,53152,57950,62978,68074,73898,79558
%N A086718 Convolution of sequence of primes with sequence sigma(n).
%C A086718 From _Omar E. Pol_, Dec 06 2021: (Start)
%C A086718 Antidiagonal sums of A272214.
%C A086718 Convolution of A000040 and A000203.
%C A086718 Convolution of A054541 and A024916.
%C A086718 Convolution of the nonzero terms of A007504 and A340793.
%C A086718 a(n) is also the volume of a tower or polycube in which the successive terraces are the symmetric representation of sigma(k), k = 1..n starting from the top, and the successive heights of the terraces are the prime numbers starting from the base. (End)
%H A086718 Robert Israel, <a href="/A086718/b086718.txt">Table of n, a(n) for n = 1..10000</a>
%p A086718 N:= 100: # to get a(1)..a(N)
%p A086718 P:= [seq(ithprime(i),i=1..N+1)]:
%p A086718 S:= [seq(numtheory:-sigma(i),i=1..N+1)]:
%p A086718 seq(add(P[i]*S[n-i],i=1..n-1),n=2..N+1); # _Robert Israel_, Sep 09 2020
%o A086718 (PARI) p=primes(30); s=vector(30,i, sigma(i)); conv(u,v)=local(w); w=vector(length(u),i,sum(j=1,i,u[j]*v[i+1-j])); w;
%o A086718 conv(p,s)
%Y A086718 Cf. A000040, A000203.
%Y A086718 Cf. A007504, A024916, A054541, A066186, A175254, A191831, A237593, A272214, A340793.
%K A086718 nonn
%O A086718 1,1
%A A086718 _Jon Perry_, Jul 29 2003
%E A086718 More terms from _Robert Israel_, Sep 09 2020