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A094949 Phi(m)*sigma(m), where m is the product of exactly two primes that differ by 2, where phi=A000010, sigma=A000203. 1
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; text; internal format)
OFFSET
1,1
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).
LINKS
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, Jul 09 2006
MATHEMATICA
EulerPhi[#]DivisorSigma[1, #]&/@Times@@@Select[Partition[Prime[ Range[ 200]], 2, 1], #[[2]]-#[[1]]==2&] (* Harvey P. Dale, Apr 13 2017 *)
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)}
CROSSREFS
Sequence in context: A051527 A305073 A101451 * A205768 A205761 A346251
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jun 19 2004
EXTENSIONS
Corrected and extended by Jason Earls, Rick L. Shepherd, Vladeta Jovovic and Klaus Brockhaus, Jun 20 2004
STATUS
approved

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Last modified April 24 05:23 EDT 2024. Contains 371918 sequences. (Running on oeis4.)