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A341655
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a(n) is the number of divisors of prime(n)^2 - 1.
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7
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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
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OFFSET
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1,1
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COMMENTS
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a(n) >= A309906(2) = 32 for n > 21.
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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Table[DivisorSigma[0, Prime[n]^2-1], {n, 66}] (* Stefano Spezia, Feb 25 2021 *)
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PROG
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(PARI) a(n) = numdiv(prime(n)^2-1); \\ Michel Marcus, Feb 25 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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