A373435 Iterate the function x <- phi(sigma(x)). The sequence lists the smaller member of cycles of length 2.

4, 48, 72, 432, 1728, 10368, 184320, 1658880, 6220800, 10222080, 12856320000

Offset

1,1

Comments

A cycle of length 2 also starts at 3852635996160. 3852635996160, 4869303828480, and 23971865863680 are also terms in the sequence. The sequence is complete through 10^13. - Jud McCranie, Sep 14 2024

166144927334400, 273145872384000, 1904394240000000,2779315686604800, 3644668394864640, 32729712349340160, 48693038284800000, 86790832128000000, 382404221337600000, 2684203735449600000, 5246585916751872000, 6169596402106368000, 13477567109529600000, 22998695842676736000, 38039819551128944640, 90555444080640000000, 102336861080974786560, 130026464870400000000, 222489728778240000000, 499064687988572160000, 2927044657152000000000, 19697331219625672704000, 23473340597403648000000, 73262977439150112768000, 1362680919097344000000000, 14128156119169341849600000, 16615689577928023080960000, 53129683677797469388800000, 6512790537509850316800000000, 125020570798295875584000000000, 201603700212193346715648000000, 1622429777898127409283072000000, 2631371767787268127693209600000, 71803515676046099742720000000000, 105852742809627160240717824000000000, 5528044915051901005564508897280000000, 15042880212263420006968149934080000000, 2013381648407800940932784726212608000000, 67868597277402193009117012867153920000000, 17285817653863442809402049534361600000000000 are also in this sequence. - Richard R. Forberg, Oct 27 2024

Links

Table of n, a(n) for n=1..11.

Example

phi(sigma(4)) = 6 and phi(sigma(6)) = 4, so 4 (the smallest term) is in the sequence.

Mathematica

Select[Range[10^6], # == EulerPhi[DivisorSigma[1, EulerPhi[DivisorSigma[1, #]]]] && # < EulerPhi[DivisorSigma[1, #]]&] (* Stefano Spezia, Jun 07 2024 *)

Prog

(PARI) isok(x) = my(y = eulerphi(sigma(x))); if (y > x, x == eulerphi(sigma(y))); \\ Michel Marcus, Jun 06 2024

Crossrefs

Subsequence of A067883 and A376256.

Cf. A000010, A000203, A062401, A001229, A095955, A095956, A373453, A373454.

Sequence in context: A242225 A157818 A362402 * A048608 A366492 A275033

Adjacent sequences: A373432 A373433 A373434 * A373436 A373437 A373438

Keyword

nonn,more

Author

Jud McCranie, Jun 06 2024

Status

approved