A068580 -id:A068580 - cp's OEIS frontend

A068581 Let phi_m(x) = phi(phi(...(phi(x))...)) m times; sequence gives values of k such that phi_4(k) = tau(k).

1, 17, 23, 29, 31, 37, 43, 51, 55, 65, 69, 77, 82, 87, 91, 93, 94, 95, 106, 111, 118, 122, 128, 129, 133, 134, 136, 142, 146, 158, 165, 170, 184, 195, 218, 230, 231, 232, 238, 243, 246, 248, 250, 254, 273, 282, 285, 286, 290, 296, 297, 310, 318, 322, 344, 351

Offset: 1

Benoit Cloitre, Mar 26 2002

Last term is a(132) = 7560.

Numbers k such that A049100(k) = A000005(k).

Jinyuan Wang, Table of n, a(n) for n = 1..132

Cf. A000005, A000010, A049100, A068579, A068580, A068582.

Select[Range[351], Nest[EulerPhi, #, 4] === DivisorSigma[0, #] &] (* Amiram Eldar, Jun 12 2022 *)

A068582 Let phi_m(x) = phi(phi(...(phi(x))...)) m times; sequence gives values of k such that phi_5(k) = tau(k).

Original entry on oeis.org

1, 41, 47, 53, 59, 61, 67, 71, 73, 79, 85, 109, 115, 119, 123, 125, 127, 141, 143, 145, 155, 159, 161, 163, 166, 177, 178, 183, 185, 194, 201, 202, 203, 206, 209, 213, 214, 215, 217, 219, 226, 237, 247, 255, 259, 262, 278, 298, 301, 302, 314, 327, 328, 343

Offset: 1

Benoit Cloitre, Mar 26 2002

Last term is a(340) = 24570.

Numbers k such that A049107(k) = A000005(k).

Jinyuan Wang, Table of n, a(n) for n = 1..340

Cf. A000005, A000010, A049107, A068579, A068580, A068581.

Select[Range[343], Nest[EulerPhi, #, 5] === DivisorSigma[0, #] &] (* Amiram Eldar, Jun 12 2022 *)

A068579 Let phi_m(x) = phi(phi(...(phi(x))...)) m times; sequence gives values of k such that phi_3(k) = tau(k).

Original entry on oeis.org

1, 11, 13, 19, 33, 34, 35, 39, 46, 57, 58, 62, 74, 86, 88, 102, 104, 105, 110, 130, 135, 138, 152, 154, 174, 182, 186, 190, 222, 258, 264, 280, 312, 330, 342, 390, 456, 462, 546, 570, 594, 756, 840, 1080

Offset: 1

Benoit Cloitre, Mar 26 2002

Numbers k such that A049099(k) = A000005(k).

Cf. A000005, A000010, A049099, A068580, A068581, A068582.

Select[Range[1080], Nest[EulerPhi, #, 3] === DivisorSigma[0, #] &] (* Amiram Eldar, Jun 12 2022 *)

is(k) = numdiv(k) == eulerphi(eulerphi(eulerphi(k))); \\ Jinyuan Wang, Apr 05 2020

cp's OEIS Frontend

A068581 Let phi_m(x) = phi(phi(...(phi(x))...)) m times; sequence gives values of k such that phi_4(k) = tau(k).

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A068582 Let phi_m(x) = phi(phi(...(phi(x))...)) m times; sequence gives values of k such that phi_5(k) = tau(k).

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A068579 Let phi_m(x) = phi(phi(...(phi(x))...)) m times; sequence gives values of k such that phi_3(k) = tau(k).

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