login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A219930 n such that phi(n) represents a new lower bound for the phi function. 2
1, 3, 8, 14, 20, 36, 48, 66, 70, 96, 126, 132, 156, 240, 252, 300, 336, 450, 480, 540, 660, 690, 714, 870, 900, 1080, 1320, 1470, 1530, 1710, 1950, 2340, 2940, 2970, 3360, 3780, 4200, 4830, 5040, 5610, 5670, 5880, 6270, 7140, 7350, 7410, 8400, 9660, 9870 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: If n is in the sequence, then the sequence contains an infinite number of multiples of n.

Conjecture: Except for 1 and 3, all members of the sequence are even. If n is odd, it cannot be squarefree.

Conjecture: There does not exist N such that for all n > N, a(n) is divisible by 30.

A036912 gives the values of the phi function at these n.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

EXAMPLE

phi(1)=1, and for n>=1, phi(n)>=1.

phi(3)=2, and for n>=3, phi(n)>=2.

phi(8)=4, and for n>=8, phi(n)>=4.

phi(14)=6, and for n>=14, phi(n)>=6.

MATHEMATICA

nn = 8!; t = Table[EulerPhi[n], {n, nn}]; min = Infinity; t2 = {}; Do[If[t[[n]] <= min, AppendTo[t2, {n, t[[n]]}]; min = t[[n]]], {n, Length[t], 1, -1}]; t2 = Reverse[t2]; t3 = {}; mx = 0; Do[If[i[[2]] > mx, mx = i[[2]]; AppendTo[t3, i[[1]]]], {i, t2}]; t3 (* T. D. Noe, Dec 04 2012 *)

PROG

(JavaScript)

p = new Array();

p[0] = NaN;

p[1] = 2;

p[2] = 3;

mj = 2;

for (k = 3; k < 50000; k += 2) makeprimes(k);

function makeprimes(i) {

for (j = 2; j <= mj; j++)

if (i%p[j] == 0) return false;

p[++mj] = i;

return true;

}

function primeFactorize(n) {

var pf = new Array(), pc, pfc;

pf[0] = new Array();

pf[1] = new Array();

pc = 1;

pfc = -1;

while (n != 1) {

if (n%p[pc] == 0) {pfc++; pf[0][pfc] = p[pc]; pf[1][pfc] = 0; }

while (n%p[pc] == 0) {n /= p[pc]; pf[1][pfc]++; }

pc++;

}

return pf;

}

function phi(n) {

var f, i, v;

v = 1;

f = primeFactorize(n);

for (i = 0; i < f[0].length; i++) v *= Math.pow(f[0][i], f[1][i] - 1)*(f[0][i] - 1);

return v;

}

function isMin(arr, ik, k) {

var i, im;

im = true;

for (i = ik; i < arr.length; i++) if (arr[i] < k) {im = false; break; }

return im;

}

phiV = new Array();

for (k = 1; k < 50000; k++) phiV[k] = phi(k);

cm = 1;

for (n = 1; n < 3000; n++) if (phiV[n] > cm && isMin(phiV, n, phiV[n])) {cm = phiV[n]; document.write(n + ", "); }

CROSSREFS

Cf. A000010, A036912, A057635, A014197.

Sequence in context: A299647 A063617 A062550 * A333962 A022947 A098762

Adjacent sequences:  A219927 A219928 A219929 * A219931 A219932 A219933

KEYWORD

nonn

AUTHOR

Jon Perry, Dec 01 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 3 10:45 EST 2021. Contains 341762 sequences. (Running on oeis4.)