A341655 a(n) is the number of divisors of prime(n)^2 - 1.
2, 4, 8, 10, 16, 16, 18, 24, 20, 32, 28, 24, 40, 32, 24, 32, 32, 32, 32, 60, 30, 48, 32, 60, 42, 48, 40, 32, 64, 48, 54, 64, 40, 64, 48, 60, 32, 40, 40, 32, 48, 96, 64, 32, 72, 90, 64, 56, 32, 64, 60, 96, 72, 96, 40, 40, 64, 96, 32, 80, 32, 48, 96, 80, 40, 32
Offset: 1
Keywords
Examples
p = factorization n prime(n) p^2 - 1 of p^2 - 1 a(n) -- -------- ------- ------------------ ---- 1 2 3 3 2 2 3 8 2^3 4 3 5 24 2^3 * 3 8 4 7 48 2^4 * 3 10 5 11 120 2^3 * 3 * 5 16 6 13 168 2^3 * 3 * 7 16 7 17 288 2^5 * 3^2 18 8 19 360 2^3 * 3^2 * 5 24 9 23 528 2^4 * 3 * 11 20 10 29 840 2^3 * 3 * 5 * 7 32 11 31 960 2^6 * 3 * 5 28 12 37 1368 2^3 * 3^2 * 19 24 13 41 1680 2^4 * 3 * 5 * 7 40 14 43 1848 2^3 * 3 * 7 * 11 32 15 47 2208 2^5 * 3 * 23 24 16 53 2808 2^3 * 3^3 * 13 32 17 59 3480 2^3 * 3 * 5 * 29 32 18 61 3720 2^3 * 3 * 5 * 31 32 19 67 4488 2^3 * 3 * 11 * 17 32 20 71 5040 2^4 * 3^2 * 5 * 7 60 21 73 5328 2^4 * 3^2 * 37 30 22 79 6240 2^5 * 3 * 5 * 13 48 23 83 6888 2^3 * 3 * 7 * 41 32 24 89 7920 2^4 * 3^2 * 5 * 11 60
Programs
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Mathematica
Table[DivisorSigma[0,Prime[n]^2-1],{n,66}] (* Stefano Spezia, Feb 25 2021 *) -
PARI
a(n) = numdiv(prime(n)^2-1); \\ Michel Marcus, Feb 25 2021
Comments