A353683 Numbers k for which phi(sigma(k)) > phi(k).

2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 28, 30, 32, 34, 36, 40, 42, 44, 46, 48, 50, 52, 54, 56, 60, 62, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 93, 94, 96, 98, 100, 102, 105, 106, 108, 110, 112, 114, 120, 124, 126, 128, 130, 132, 136, 138, 140, 142, 144, 148, 150, 152, 154, 156, 160

Offset

1,1

Comments

Numbers k such that A062401(k) > A000010(k).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n)

Maple

filter:= proc(k) uses NumberTheory;
    phi(sigma(k)) > phi(k)
end proc:
select(filter, [$1..200]); # Robert Israel, Feb 24 2026

Mathematica

Select[Range[160], EulerPhi[DivisorSigma[1, #]] > EulerPhi[#] &] (* Amiram Eldar, May 06 2022 *)

Prog

(PARI)
A353681(n) = (eulerphi(sigma(n))>eulerphi(n));
isA353683(n) = A353681(n);

Crossrefs

Positions of strictly positive terms in A353636.

Cf. A000010, A000203, A062401, A353681 (characteristic function), A353685 (complement).

Setwise difference of A353684 and A006872.

Sequence in context: A355529 A355670 A336375 * A296214 A325572 A337945

Adjacent sequences: A353680 A353681 A353682 * A353684 A353685 A353686

Keyword

nonn

Author

Antti Karttunen, May 06 2022

Status

approved