A372670 Numbers k such that k * phi(k) is a fifth power.

1, 8, 256, 500, 864, 8192, 9826, 16000, 27648, 54000, 132651, 209952, 246924, 262144, 314432, 333396, 512000, 884736, 1061208, 1562500, 1728000, 6718464, 7002306, 7294032, 7901568, 8388608, 8541936, 10061824, 10668672, 13122000, 13564278, 15432750, 16384000

Offset

1,2

Comments

To look for terms it suffices to see if fifth powers have a divisors pair (k, m) such that phi(m) = k. - David A. Corneth, May 21 2024

Links

David A. Corneth, Table of n, a(n) for n = 1..8846 (first 38 terms from R. J. Mathar)

Formula

If n is in the sequence and prime p divides n, then p^5*n is in the sequence.

Example

8 * phi(8) = 32 = 2^5.

Prog

(PARI) isok(n) = ispower(n*eulerphi(n), 5);

Crossrefs

Cf. A000584, A002618, A114076.

Sequence in context: A034674 A317511 A300176 * A291850 A130034 A128787

Adjacent sequences: A372667 A372668 A372669 * A372671 A372672 A372673

Keyword

nonn

Author

Seiichi Manyama, May 10 2024

Status

approved