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Search: id:A123113
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| A123113 |
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Main diagonal of prime power sum array. |
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+0
6
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| 2, 13, 280, 17489, 48909526, 13423779037, 232729381165100, 146367546237420097, 8864305651125125485354, 100000100010100010100010101101, 193529735150413879906083607547512
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also see A062481 a(n)=n^p(n)=A000027(n)^A000040(n). A(n,n) is prime for n = 1, 2, 4 -- what is the next prime in the sequence?
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FORMULA
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a(n) = 1 + n^2 + n^3 + n^5 + ... + n^prime(n). = Main diagonal A(n,n), of the infinite array A(k,n) = 1 + SUM[i=1..k]n^prime(i). If we deem prime(0) = 1, the array is A(k,n) = SUM[i=0..k]n^prime(i).
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EXAMPLE
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a(1) = 2 = 1+1^2.
a(2) = 13 = 1+2^2+2^3.
a(3) = 280 = 1+3^2+3^3+3^5.
a(4) = 17489 = 1+4^2+4^3+4^5+4^7.
a(5) = 48909526 = 1+5^2+5^3+5^5+5^7+5^11.
a(6) = 13423779037 = 1+6^2+6^3+6^5+6^7+6^11+6^13.
a(7) = 232729381165100 = 1+7^2+7^3+7^5+7^7+7^11+7^13+7^17.
a(8) = 146367546237420097 = 1+8^2+8^3+8^5+8^7+8^11+8^13+8^17+8^19.
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CROSSREFS
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Cf. A000027, A000040, A062481.
Sequence in context: A042677 A134296 A086510 this_sequence A126742 A013051 A012955
Adjacent sequences: A123110 A123111 A123112 this_sequence A123114 A123115 A123116
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 28 2006
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