A300216 Numbers k such that k and phi(k) share the same prime signature.
1, 3, 14, 22, 28, 44, 46, 50, 56, 88, 92, 94, 112, 118, 166, 176, 184, 188, 198, 214, 224, 236, 294, 332, 334, 352, 358, 368, 376, 414, 428, 448, 454, 472, 500, 526, 664, 668, 694, 704, 716, 718, 726, 736, 752, 766, 846, 856, 882, 896, 908, 934, 944, 958, 1006
Offset: 1
Keywords
Examples
1 is a term since phi(1) is 1. The prime signature of 1 is 0 or the empty set {0}.
3 is a term since phi(3)=2 and both are prime, hence prime signature is {1}.
14 is a term since phi(14)=6 and 14 and 6 are both the product of two distinct primes and the prime signature is {1,1}.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
Programs
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Maple
s:= n-> sort(map(i-> i[2], ifactors(n)[2])): a:= proc(n) option remember; local k; for k from 1+ a(n-1) while s(k)<>s(numtheory[phi](k)) do od; k end: a(0):=0: seq(a(n), n=1..60); # Alois P. Heinz, Feb 28 2018 -
Mathematica
s[k_] := Sort[FactorInteger[k][[All, 2]]]; filterQ[k_] := Switch[k, 2, False, 3, True, _, s[k] == s[EulerPhi[k]]]; Select[Range[2000], filterQ] (* Jean-François Alcover, Oct 28 2020 *)
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PARI
isok(k) = vecsort(factor(k)[,2]) == vecsort(factor(eulerphi(k))[,2]); \\ Michel Marcus, Mar 09 2018
Comments