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A086718
Convolution of sequence of primes with sequence sigma(n).
4
2, 9, 22, 48, 85, 151, 231, 355, 500, 709, 937, 1267, 1617, 2069, 2575, 3193, 3860, 4686, 5549, 6593, 7725, 8985, 10337, 11961, 13591, 15464, 17498, 19714, 22036, 24690, 27378, 30382, 33603, 37023, 40597, 44733, 48720, 53152, 57950, 62978, 68074, 73898, 79558
OFFSET
1,1
COMMENTS
From Omar E. Pol, Dec 06 2021: (Start)
Antidiagonal sums of A272214.
Convolution of A000040 and A000203.
Convolution of A054541 and A024916.
Convolution of the nonzero terms of A007504 and A340793.
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)
LINKS
MAPLE
N:= 100: # to get a(1)..a(N)
P:= [seq(ithprime(i), i=1..N+1)]:
S:= [seq(numtheory:-sigma(i), i=1..N+1)]:
seq(add(P[i]*S[n-i], i=1..n-1), n=2..N+1); # Robert Israel, Sep 09 2020
PROG
(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;
conv(p, s)
KEYWORD
nonn
AUTHOR
Jon Perry, Jul 29 2003
EXTENSIONS
More terms from Robert Israel, Sep 09 2020
STATUS
approved