login

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 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Totient superdeficient numbers: numbers n > 1 such that s(n)/n < s(m)/m for all m < n, where s(n) is the sum of iterated phi(n) (A092693).
1

%I #9 Aug 31 2017 17:43:38

%S 2,42,90,210,630,1050,1470,2310,6930,16170,30030,90090,150150,210210,

%T 570570,690690,870870,2072070,3573570,3993990,4834830

%N Totient superdeficient numbers: numbers n > 1 such that s(n)/n < s(m)/m for all m < n, where s(n) is the sum of iterated phi(n) (A092693).

%C A variation of A286268 (Totient superabundant numbers).

%e The values of A092693(n)/n for n = 2, 42, 90 are 0.5, 0.452..., 0.433..., which are records of lowest values.

%t Function[s, Flatten[First@Position[s, #] & /@ Union@Rest@FoldList[Max, 0, s]]]@ Table[n/(Total@FixedPointList[EulerPhi, n] - (n + 1)), {n, 2, 10^5}]+1 (* after _Michael De Vlieger_ at A286268 and _Alonso del Arte_ at A092693 *)

%Y Cf. A092693, A286268, A291174.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Aug 19 2017