A050934 Numbers k such that phi(k)*d(k) is a multiple of sigma(k), where d(k) is the number of divisors of k.

1, 3, 14, 35, 42, 105, 209, 248, 297, 418, 594, 627, 744, 1045, 1254, 1485, 1736, 2926, 3135, 3339, 3596, 3689, 3956, 4064, 4158, 5208, 5396, 5890, 6461, 7315, 7668, 8370, 8636, 8680, 8778, 8932, 9875, 10013, 10395, 10788, 11067, 11687

Offset

1,2

Comments

Equality holds for 1, 3, 14, 42 and no others < 4290000000.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

phi(35)*d(35) = 4*24, a multiple of sigma(35) = 48, so 35 is in the sequence.

Mathematica

Select[Range[12000], Divisible[EulerPhi[#]DivisorSigma[0, #], DivisorSigma[ 1, #]]&] (* Harvey P. Dale, Jan 11 2019 *)

Prog

(PARI) is(n) = {my(f = factor(n)); !((eulerphi(f) * numdiv(f)) % sigma(f)); } \\ Amiram Eldar, Apr 04 2024

Crossrefs

Cf. A000005 (d), A000010 (phi), A000203 (sigma).

Sequence in context: A076533 A081379 A081377 * A110427 A296294 A128916

Adjacent sequences: A050931 A050932 A050933 * A050935 A050936 A050937

Keyword

nonn

Author

Jud McCranie, Dec 30 1999

Status

approved