A126106 -id:A126106 - cp's OEIS frontend

A181659 Numbers at which the sum of the iterated totient function (A092693) attains a record.

1, 2, 3, 5, 7, 11, 13, 17, 23, 29, 37, 41, 47, 53, 59, 71, 73, 79, 83, 89, 101, 107, 131, 137, 167, 179, 227, 233, 257, 289, 317, 347, 359, 389, 443, 449, 461, 467, 503, 557, 563, 569, 587, 641, 719, 809, 839, 857, 929, 977, 983, 1013, 1019, 1097, 1187, 1193, 1283

Offset: 1

T. D. Noe, Nov 04 2010

nonn

Most of these numbers are prime. The first four composites are 289, 2329, 4369, and 4913.

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A181660

Cf. A126106 (record values)

kMax=2*3*5*7*11*13; t=Table[0,{kMax}]; Do[e=EulerPhi[k]; t[[k]]=e+t[[e]], {k,2,kMax}]; mx=-1; Reap[Do[If[t[[k]]>mx, mx=t[[k]]; Sow[k]], {k,kMax}]][[2,1]]

A332737 Composite terms of A181659, where the sum of the iterated totient function attains a record.

Original entry on oeis.org

289, 2329, 4369, 4913, 18769, 21331, 35209, 66049, 128881, 197143, 258121, 281929, 516961, 739903, 971203, 1762249, 1942663, 2070721, 2898703, 2952673, 3820819, 4142881, 8288641, 16773619, 16843009, 16974593, 20229241, 21762361, 32472241, 132575071, 187903693

Offset: 1

Amiram Eldar, Feb 21 2020

nonn

Most of the terms of A181659 are primes. Out of the first 10^4 terms of A181659 only 28 are composites.
The indices of the terms of this sequence in A181659 are 30, 73, 93, 99, 154, 161, 191, 236, 286, 316, ...
The corresponding record values (terms of A126106) are 527, 4223, 8191, 8847, 35527, 39423, 67583, 131327, 246869, 376559, 493739, 550911, 1009981, 1466879, 1884671, 3442687, 3819519, 4089245, 5707263, 5791743, 7444991, 8178491, 16464253, 33260031, 33554431, 33718527, 39989247, 42809067, 63932219, 263382015, 372697723.

Cf. A092693, A126106, A181659.

s[n_] := Plus @@ FixedPointList[EulerPhi, n] - n - 1; seq={}; smax = 1; Do[s1 =s[n];  If[s1 >smax, smax = s1; If[CompositeQ[n], AppendTo[seq, n]]], {n, 1,  5000}]; seq

cp's OEIS Frontend

A181659 Numbers at which the sum of the iterated totient function (A092693) attains a record.

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