A215240 -id:A215240 - cp's OEIS frontend

A320041 Primes that are values of A215240.

3, 13, 6163, 8311, 12097, 13159, 14957, 18433, 21061, 23627, 24571, 27061, 29863, 35617, 40897, 44221, 45307, 45737, 45821, 67421, 68113, 69313, 71237, 75377, 82903, 89227, 89269, 89671, 94543, 100483, 101533, 101833, 113683, 114827, 118903, 121763, 122167, 125933, 131581, 131617, 143461, 144061

Offset: 1

Robert Israel and J. M. Bergot, Oct 03 2018

nonn

Values of A215240(A320061), sorted.

			a(3) = 6163 is in the sequence because it is prime and A215240(264) = 6163.

Robert Israel, Table of n, a(n) for n = 1..594

Cf. A215240, A320061.

N:= 10^5: # to get all terms <= N
f:= n -> convert(numtheory:-invphi(n),`+`):
Res:= {}:
for n from 1 to N do
  v:= f(n);
  if isprime(v) and v <= N then
     Res:= Res union {v}
  fi
od:
Res;

A320061 Numbers k such that A215240(k) is prime.

Original entry on oeis.org

1, 2, 144, 264, 540, 720, 888, 928, 1012, 1368, 1452, 1476, 1656, 1764, 1800, 1836, 1960, 2024, 2392, 2664, 2712, 2968, 3444, 3680, 3720, 3808, 4248, 4284, 4352, 4368, 4776, 5060, 5412, 5600, 6516, 6624, 6840, 6984, 7040, 7168, 7176, 7600, 7836, 7860, 8052, 8160, 8196, 8304, 8496, 8848, 9144

Offset: 1

Robert Israel, Oct 04 2018

nonn

			a(3)=144 is in the sequence because phi(h)=144 for h = 185, 219, 273, 285, 292, 296, 304, 315, 364, 370, 380, 432, 438, 444, 456, 468, 504, 540, 546, 570, 630, and the sum of those is the prime 8311.

Robert Israel, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI scripts for various problems (see invphi.gp there).

Cf. A215240, A320041.

select(n -> isprime(convert(numtheory:-invphi(n),`+`)), [$1..10000]);

isok(n) = isprime(vecsum(invphi(n))); \\ Michel Marcus, Oct 05 2018

A217842 Product of the numbers p such that phi(p) = n, where phi is Euler's totient function.

Original entry on oeis.org

2, 72, 1, 4800, 1, 15876, 1, 3456000, 1, 242, 1, 300500928, 1, 1, 1, 2130739200, 1, 1052676, 1, 119790000, 1, 1058, 1, 531598161669120000, 1, 1, 1, 1682, 1, 1922, 1, 20864198246400, 1, 1, 1, 1159208596538496, 1, 1, 1, 265804426800000000, 1, 17757796, 1

Offset: 1

T. D. Noe, Oct 12 2012

nonn

It appears that all terms greater than 1 are distinct. This is true for all n <= 10^6.

T. D. Noe, Table of n, a(n) for n = 1..1000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
David M. Bressoud, A Course in Computational Number Theory (web page), CNT.m, Computational Number Theory Mathematica package.

Cf. A002181 (smallest inverse), A006511 (largest inverse), A215240 (sum of inverses).

Cf. A032447 (inverse of phi).

Needs["CNT`"]; Table[Times @@ PhiInverse[n], {n, 100}]

a(n) = vecprod(invphi(n)); \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp

cp's OEIS Frontend

A320041 Primes that are values of A215240.

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Maple

A320061 Numbers k such that A215240(k) is prime.

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Author

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Maple

PARI

A217842 Product of the numbers p such that phi(p) = n, where phi is Euler's totient function.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI