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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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)

Crossrefs

Cf. A000040, A000203.

Cf. A007504, A024916, A054541, A066186, A175254, A191831, A237593, A272214, A340793.

Sequence in context: A323891 A212069 A106058 * A023625 A166754 A026589

Adjacent sequences: A086715 A086716 A086717 * A086719 A086720 A086721

Keyword

nonn

Author

Jon Perry, Jul 29 2003

Extensions

More terms from Robert Israel, Sep 09 2020

Status

approved