A234542 Positive integer solutions to sigma(sigma(k) - k - 3)/phi(k - phi(k) + 3) = 3.

15, 35, 68, 95, 119, 143, 155, 188, 203, 280, 289, 299, 323, 371, 395, 611, 695, 731, 779, 791, 803, 851, 899, 923, 959, 995, 1055, 1139, 1146, 1199, 1355, 1369, 1379, 1391, 1403, 1424, 1643, 1703, 1739, 1751, 1763, 1883, 1895, 1919, 2051, 2123, 2159, 2231, 2471, 2483, 2723, 2759, 2809

Offset: 1

Author

Wesley Ivan Hurt, Dec 27 2013

Keywords

• nonn

Comments

If n is the product of a pair of twin primes (A037074), then n is in the sequence (The first few terms of A037074 are: 15, 35, 143, 323, 899, 1763, 3599, ..). For these numbers, the numerator is equal to 3*sqrt(n + 1) and the denominator (A186749) is equal to sqrt(n + 1), giving 3 as a result.

Examples

			119 appears in the sequence since sigma(sigma(119) - 119 - 3)/phi(119 - phi(119) + 3) = sigma(22)/phi(26) = 36/12 = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A001065, A037074, A051953, A186749.

Programs

Maple

with(numtheory); A234542:=n->`if`(sigma(sigma(n)-n-3)/phi(n-phi(n)+3)=3,n,NULL); seq(A234542(n), n=1..5000);

Mathematica

Select[Range[1000], DivisorSigma[1, DivisorSigma[1, #] - # - 3]/EulerPhi[# - EulerPhi[#] + 3] == 3 &] (* Alonso del Arte, Jan 01 2014 *)

Formula

Solutions to A000203(A001065(k) - 3)/A000010(A051953(k) + 3) = 3.