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

Author

Jud McCranie, Jun 06 2024

Keywords

• nonn
• more

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

Examples

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

Crossrefs

Subsequence of A067883 and A376256.

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

Programs

Mathematica

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

PARI

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