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A094949
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Phi(m)*sigma(m), where m is the product of exactly two primes that differ by 2, where phi=A000010, sigma=A000203.
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0
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192, 1152, 20160, 103680, 806400, 3104640, 12945600, 26853120, 108201600, 136002240, 362597760, 506160000, 1049630400, 1358807040, 1536796800, 2702128320, 3317529600, 5314118400, 6323748480, 9475464960, 14665694400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If m=p*q for the twin prime pair (p, q), then the relation p^2 + q^2 = 2*(m+2) is evident from equations p*(p+2)=m=q*(q-2). Now phi(m)=(p-1)*(q-1)=p^2 - 1 and sigma(m)=(p+1)*(q+1)=q^2 - 1, so that phi(m)*sigma(m)=(p*q)^2 -(p^2 + q^2)+1=m^2-2*(m+2)+1=(m-3)*(m+1).
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FORMULA
| a(n)=(m-3)*(m+1), where m=A037074(n).
a(n)=192*A002415(k), where k=A040040(n-1).
a(n) = (A120875(n))^2 - 4 = 4*{(A120876(n)^2 - 1}. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 09 2006
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PROG
| (PARI) {m=400; p=1; while(p<m, p=nextprime(p); q=nextprime(p+1); if(p+2==q, r=p*q; print1(eulerphi(r)*sigma(r), ", ")); p=q)}
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CROSSREFS
| Cf. A001359, A006512, A037074.
Sequence in context: A054001 A051527 A101451 * A205768 A205761 A133064
Adjacent sequences: A094946 A094947 A094948 * A094950 A094951 A094952
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 19 2004
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EXTENSIONS
| Corrected and extended by Jason Earls (zevi_35711(AT)yahoo.com), Rick L. Shepherd (rshepherd2(AT)hotmail.com), Vladeta Jovovic (vladeta(AT)eunet.rs) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 20 2004
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