A122483 Numbers m such that A049060(m)*sigma(m) = k*uphi(m)*m for some integer k.

6, 140, 312, 1560, 14384, 18018, 40992, 2337400, 7012200, 11027016, 231402600, 534775296, 9866296440, 11453072202

Offset: 1

Author

Yasutoshi Kohmoto, Sep 30 2006

Keywords

• nonn
• more

Comments

If both 2^n-3 and 2^n-1 are prime then numbers of the form 2^(n-1)*(M_n-2)*M_n appear in the sequence, where M_n means Mersenne prime.

Examples

			2^8*7*19*37*73*509, 2^8*5*7*19*37*509, 2^8*5^2*7*19*29*31*37*509, 2^9*3*11*31*1021, 2^9*3*7*11^2*19*31*131*1021, 2^11*3^6*5*7*13*23*137*467*1093*4093, 2^13*3*11*43*127*16381, 2^13*3*7*11^2*19*43*127*131*16381 are terms, but there may be many other terms between 3*10^7 and them.
		

Crossrefs

Cf. A123124, A000203 (sigma), A047994 (uphi), A049060.

Programs

Mathematica

f[p_, e_] := (p^(e+1)-2*p+1) * (p^(e+1)-1)/((p-1)^2 * (p^e - 1)); q[n_] := IntegerQ[(Times @@ f @@@ FactorInteger[n])/n]; Select[Range[2, 10^5], q] (* Amiram Eldar, Sep 19 2022 *)

Extensions

More terms from R. J. Mathar, Oct 01 2006

a(12)-a(14) from Amiram Eldar, Sep 19 2022