A094949 Phi(m)*sigma(m), where m is the product of exactly two primes that differ by 2, where phi=A000010, sigma=A000203.

192, 1152, 20160, 103680, 806400, 3104640, 12945600, 26853120, 108201600, 136002240, 362597760, 506160000, 1049630400, 1358807040, 1536796800, 2702128320, 3317529600, 5314118400, 6323748480, 9475464960, 14665694400

Offset: 1

Author

Lekraj Beedassy, Jun 19 2004

Keywords

• nonn

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

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359, A006512, A037074.

Programs

Mathematica

EulerPhi[#]DivisorSigma[1,#]&/@Times@@@Select[Partition[Prime[ Range[ 200]],2,1],#[[2]]-#[[1]]==2&] (* Harvey P. Dale, Apr 13 2017 *)

PARI

{m=400;p=1;while(p
				

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

Extensions

Corrected and extended by Jason Earls, Rick L. Shepherd, Vladeta Jovovic and Klaus Brockhaus, Jun 20 2004