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A161993
A006005 (shifted) convolved with all of its regularly "aerated" variants.
1
1, 3, 8, 19, 43, 85, 171, 315, 580, 1022, 1766, 2982, 4959, 8081, 12997, 20596, 32261, 49909, 76447, 115872, 174133, 259312, 383206, 561877, 818225, 1183266, 1700658, 2429266, 3450562, 4874167, 6850072, 9578548, 13331445, 18469783, 25478494, 34999375, 47887091
OFFSET
0,2
COMMENTS
Refer to A161779 for the analogous sequence based on the factorials.
Given A006005 (1 together with the odd primes = odd noncomposite numbers) = a, then b = the aerated variant: (1, 0, 3, 0, 5, 0, 7,...); c = (1, 0, 0, 3, 0, 0, 5,...) and so on such that A161993 = the infinite convolution product: a*b*c*...
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..5000 from Alois P. Heinz)
MAPLE
p:= n-> `if`(n=0, 1, ithprime(n+1)):
b:= proc(n, i) option remember; `if`(i>n, 0,
`if`(irem(n, i, 'r')=0, p(r), 0)+
add(p(j)*b(n-i*j, i+1), j=0..n/i))
end:
a:= n-> `if`(n=0, 1, b(n, 1)):
seq(a(n), n=0..45); # Alois P. Heinz, Jul 27 2019
MATHEMATICA
p[n_] := If[n==0, 1, Prime[n+1]];
b[n_, i_] := b[n, i] = If[i>n, 0, If[Mod[n, i]==0, p[n/i], 0] + Sum[p[j] b[n - i j, i+1], {j, 0, n/i}]];
a[n_] := If[n==0, 1, b[n, 1]];
a /@ Range[0, 45] (* Jean-François Alcover, Nov 20 2020, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A357291 A099050 A065352 * A360489 A259401 A008466
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jun 24 2009
EXTENSIONS
Definition and comment corrected by Omar E. Pol, Aug 18 2011
Correct offset and a(13)-a(36) from Alois P. Heinz, Jul 27 2019
STATUS
approved