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Number of divisors of 12^n+1.
+10
14
2, 2, 4, 8, 4, 4, 8, 8, 8, 32, 12, 4, 16, 24, 16, 128, 4, 8, 32, 16, 64, 384, 64, 16, 64, 64, 32, 1024, 8, 8, 48, 8, 4, 512, 16, 32, 128, 16, 32, 1536, 16, 32, 64, 32, 16, 4096, 8, 32, 32, 32, 512, 512, 32, 32, 1024, 128, 512, 1536, 192, 64, 1024, 32, 64
a(n) = phi(12^n+1), where phi is Euler's totient function ( A000010).
+10
14
1, 12, 112, 1296, 20416, 229680, 2306304, 32916240, 400515072, 3863116800, 47825825600, 685853880624, 8732596764672, 97509650382144, 990242755633152, 11148606564480000, 184883057981234176, 2047145911595946000, 20281543142263603200, 294779525244632305920
Sum of the divisors of 12^n+1.
+10
13
3, 14, 180, 2240, 21060, 267988, 3706920, 38773952, 459970056, 6692483840, 79425033660, 800162860756, 9101898907920, 117326869641600, 1596198064568400, 20655000929239040, 184885459808838660, 2390210102271311936, 33504016991491136160, 344201347103878781440
Smallest prime dividing 4^n + 1.
+10
8
2, 5, 17, 5, 257, 5, 17, 5, 65537, 5, 17, 5, 97, 5, 17, 5, 641, 5, 17, 5, 257, 5, 17, 5, 193, 5, 17, 5, 257, 5, 17, 5, 274177, 5, 17, 5, 97, 5, 17, 5, 65537, 5, 17, 5, 257, 5, 17, 5, 641, 5, 17, 5, 257, 5, 17, 5, 449, 5, 17, 5, 97, 5, 17, 5, 59649589127497217
Number of prime factors of 12^n + 1 (counted with multiplicity).
+10
8
1, 1, 2, 3, 2, 2, 3, 3, 3, 5, 4, 2, 4, 5, 4, 7, 2, 3, 5, 4, 6, 9, 6, 4, 6, 6, 5, 10, 3, 3, 6, 3, 2, 9, 4, 5, 7, 4, 5, 11, 4, 5, 6, 5, 4, 12, 3, 5, 5, 5, 10, 9, 5, 5, 10, 7, 9, 11, 8, 6, 10, 5, 6, 15, 5, 9, 11, 4, 5, 12, 10, 3, 10, 5, 8, 17, 5, 6, 9, 4, 6, 15
Largest prime factor of 12^n+1.
+10
7
2, 13, 29, 19, 233, 19141, 20593, 13063, 260753, 1801, 85403261, 57154490053, 2227777, 222379, 13156924369, 35671, 1200913648289, 66900193189411, 122138321401, 905265296671, 67657441, 1885339, 68368660537, 49489630860836437, 592734049, 438472201
Smallest prime dividing 6^n + 1.
+10
6
2, 7, 37, 7, 1297, 7, 13, 7, 17, 7, 37, 7, 1297, 7, 37, 7, 353, 7, 13, 7, 41, 7, 37, 7, 17, 7, 37, 7, 281, 7, 13, 7, 2753, 7, 37, 7, 577, 7, 37, 7, 17, 7, 13, 7, 89, 7, 37, 7, 193, 7, 37, 7, 1297, 7, 13, 7, 17, 7, 37, 7, 41, 7, 37, 7, 4926056449, 7, 13, 7, 137
Smallest prime dividing 8^n + 1.
+10
5
2, 3, 5, 3, 17, 3, 5, 3, 97, 3, 5, 3, 17, 3, 5, 3, 193, 3, 5, 3, 17, 3, 5, 3, 97, 3, 5, 3, 17, 3, 5, 3, 641, 3, 5, 3, 17, 3, 5, 3, 97, 3, 5, 3, 17, 3, 5, 3, 193, 3, 5, 3, 17, 3, 5, 3, 97, 3, 5, 3, 17, 3, 5, 3, 769, 3, 5, 3, 17, 3, 5, 3, 97, 3, 5, 3, 17, 3, 5
Smallest prime dividing 12^n - 1.
+10
5
11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11
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