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Search: id:A072779
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| A072779 |
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Sigma2[n] + Phi[n] Sigma[n]. |
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+0
2
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| 2, 8, 18, 35, 50, 74, 98, 145, 169, 202, 242, 322, 338, 394, 452, 589, 578, 689, 722, 882, 884, 970, 1058, 1330, 1271, 1354, 1540, 1722, 1682, 1876, 1922, 2373, 2180, 2314, 2452, 3003, 2738, 2890, 3044, 3650, 3362, 3652, 3698, 4242, 4238, 4234, 4418
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence is interesting because (1) a(n) >= 2 n^2, with equality only when n is prime (or 1) and (2) a(n) = 2 + 2 n^2 if and only if n is the product of two distinct primes. Note for twin primes: let n = m^2 - 1, then m-1 and m+1 are twin primes if and only if a(n) = 2 + 2 n^2. Note for the Goldbach conjecture: let n = m^ 2 - r^2, then m-r and m+r are primes that add to 2m if and only if a(n) = 2 + 2 n^2. See A072780 for a(n) - 2 n^2.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Divisor Function
Eric Weisstein's World of Mathematics, Totient Function
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MATHEMATICA
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Table[DivisorSigma[2, n]+EulerPhi[n]DivisorSigma[1, n], {n, 100}]
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CROSSREFS
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Cf. A072780, A065387.
Sequence in context: A050804 A018229 A166830 this_sequence A064705 A058858 A073307
Adjacent sequences: A072776 A072777 A072778 this_sequence A072780 A072781 A072782
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KEYWORD
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easy,nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 15 2002
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