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A267217
10-gonal (or decagonal) numbers with prime indices.
0
10, 27, 85, 175, 451, 637, 1105, 1387, 2047, 3277, 3751, 5365, 6601, 7267, 8695, 11077, 13747, 14701, 17755, 19951, 21097, 24727, 27307, 31417, 37345, 40501, 42127, 45475, 47197, 50737, 64135, 68251, 74665, 76867, 88357, 90751, 98125, 105787, 111055, 119197, 127627, 130501, 145351, 148417, 154645
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Decagonal Number
Eric Weisstein's World of Mathematics, Prime Number
FORMULA
a(n) = prime(n)*(4*prime(n) - 3) = A000040(n)*(4*A000040(n) - 4).
a(n) = A001107(A000040(n)).
a(n) = sigma_0(48^(prime(n) - 1)) = A000005(A009992(A000040(n) - 1)).
MATHEMATICA
Table[Prime[n] (4 Prime[n] - 3), {n, 1, 45}]
Module[{nn=200, pn}, pn=PolygonalNumber[10, Range[nn]]; Table[pn[[p]], {p, Prime[ Range[PrimePi[nn]]]}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 27 2020 *)
PROG
(PARI) lista(nn) = forprime(p=2, nn, print1(p*(4*p-3), ", ")); \\ Altug Alkan, Jan 12 2016
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Jan 12 2016
STATUS
approved