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Search: id:A123650
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| 4, 45, 280, 1105, 3276, 8029, 17200, 33345, 59860, 101101, 162504, 250705, 373660, 540765, 762976, 1052929, 1425060, 1895725, 2483320, 3208401, 4093804, 5164765, 6449040, 7977025, 9781876, 11899629, 14369320, 17233105, 20536380, 24327901
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OFFSET
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1,1
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COMMENT
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3rd row, A(3,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). The first row is A002522 = 1 + n^2. The second row is A098547 = 1 + n^2 + n^3. The 4th row, A(4,n), is A123111 1+n^2+n^3+n^5+n^7. 10101101 (base n). A(n,n) is A123113 Main diagonal of prime power sum array. The current sequence, A(3,n), can never be prime because of the polynomial factorization a(n) = 1 + n^2 + n^3 + n^5 = +/- (n+1)*(n^2-n+1)*(n^2+1). Its fewest prime factors are 2 for the semiprime a(1) = 4. We similarly have polynomial factorizations for A123651 = A(7,n) = 1+n^2+n^3+n^5+n^7+n^11+n^13+n^17 and A123652 = A(13,n) = 1+n^2+n^3+n^5+...+n^41.
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FORMULA
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a(n) = 1 + n^2 + n^3 + n^5 = 101101 (base n) = +/- (n+1)*(n^2-n+1)*(n^2+1).
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CROSSREFS
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Cf. A002522, A098547, A123111, A123113, A123651, A123652.
Adjacent sequences: A123647 A123648 A123649 this_sequence A123651 A123652 A123653
Sequence in context: A070225 A132998 A120075 this_sequence A122910 A117644 A055602
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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), Oct 04 2006
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