A091495 -id:A091495 - cp's OEIS frontend

A036798 Odd numbers m such that there exists an even number k < m with phi(k) = phi(m).

105, 165, 195, 315, 495, 525, 585, 735, 825, 945, 975, 1155, 1365, 1485, 1575, 1755, 1785, 1815, 1995, 2145, 2205, 2415, 2475, 2535, 2625, 2805, 2835, 2925, 3003, 3045, 3135, 3255, 3315, 3465, 3675, 3705, 3795, 3885, 3927, 4095, 4125, 4305, 4389, 4455

Offset: 1

David W. Wilson

nonn

These numbers m appear to satisfy cototient(m) > totient(m) or 2*phi(m) < m; they seem to be the missing terms mentioned in A067800. - Labos Elemer, May 08 2003
All elements in this sequence must have 2*phi(m) < m, but not the reverse. See A118700. - Franklin T. Adams-Watters, May 21 2006
The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 11, 108, 1139, 11036, 111796, ... . Apparently, the asymptotic density of this sequence exists and equals 0.011... . - Amiram Eldar, Nov 21 2024

Robert Israel, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A000010, A067800, A083254.
Cf. A091495 (Odd, squarefree n such that n/phi(n) > 2).
Cf. A118700, A119434.

N:= 10^4: # to get all terms <= N
PhiE:= map(numtheory:-phi, [seq(i,i=2..N,2)]):
A:= NULL:
for n from 1 to N by 2 do
t:= numtheory:-phi(n);
if 2*t < n and member(t, PhiE[1..(n-1)/2]) then A:= A,n fi;
od:
A; # Robert Israel, Jan 06 2017

is(m) = m%2 && #select(k -> !(k%2) && k < m, invphi(eulerphi(m))) > 0; \\ Amiram Eldar, Nov 21 2024, using Max Alekseyev's invphi.gp

A215130 Odd squarefree n not divisible by 3 such that n/phi(n) > 2, where phi is Euler's totient function.

Original entry on oeis.org

37182145, 46881835, 50115065, 59814755, 1078282205, 1152646495, 1375739365, 1453336885, 1524467945, 1598832235, 1734627895, 1747560815, 1759302545, 1854257405, 1922155235, 1966279315, 1970653685, 2015918905, 2054717665, 2099812715, 2154947795, 2193746555

Offset: 1

Donovan Johnson, Aug 04 2012

nonn

Terms in A091495 not divisible by 3.

The first 5000 terms are divisible by both 5 and 7. a(2276) = 112435426285 is the smallest term not divisible by 11. - Donovan Johnson, Nov 03 2013

Donovan Johnson, Table of n, a(n) for n = 1..5000

Cf. A091495, A000010.

forstep(n=1, 2193746557, [4,2], if(issquarefree(n), if(n/eulerphi(n)>2, print1(n ", "))))

cp's OEIS Frontend

A036798 Odd numbers m such that there exists an even number k < m with phi(k) = phi(m).

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