The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A071348 Intersection of A068017 and A068019]: numbers n such that both sigma[n] and phi[n] are middle terms between (different) twin prime pairs. 1
 10, 26, 38, 135, 206, 209, 216, 278, 371, 398, 416, 545, 560, 650, 698, 792, 866, 924, 1062, 1125, 1286, 1364, 1403, 1482, 1512, 1946, 2021, 2151, 2306, 2432, 2516, 2920, 3040, 3239, 3263, 3338, 3363, 3398, 3443, 3537, 3758, 3815, 4028, 4041, 4058, 4131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 5 is not a term. Sigma=6, and both 6-1=5 and 6+1=7 are primes. Phi=4, and both 4-1=3 and 4+1=5 are primes. But, even though (3,5) and (5,7) are in some sense "(different) twin prime pairs" (quoting the sequence's definition), because 5 is a member of both they are treated, for purposes of this sequence, as not being "different." - Harvey P. Dale, Jun 05 2019 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE n=4440,6328,6808,7030: sigma[n]=13680 between 13679 and 13681 prime, while Phi=1152,Phi=2688,Phi=3168,Phi=2592 are middle terms between different twin-pairs; n=545,866,1482,1512: phi[n]=432 between 431 and 433; sigma[n]-s give middle terms between different twin prime pairs. MATHEMATICA Do[s=-1+DivisorSigma[1, n]; s1=1+DivisorSigma[1, n]; z=-1+EulerPhi[n]; z1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&& PrimeQ[z]&&PrimeQ[z1]&&!PrimeQ[n], Print[{n, s, s1, z, z1}]], {n, 1, 10000}] spmtQ[n_]:=Module[{s=DivisorSigma[1, n], p=EulerPhi[n]}, s!=p&&AllTrue[ {s+1, s-1, p+1, p-1}, PrimeQ]]; Select[Range[6, 4200], spmtQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 05 2019 *) CROSSREFS Cf. A000010, A000203, A068017, A068019. Sequence in context: A045039 A322972 A080059 * A055042 A044071 A186279 Adjacent sequences:  A071345 A071346 A071347 * A071349 A071350 A071351 KEYWORD nonn AUTHOR Labos Elemer, May 21 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)