Math::N...Perfect(3)

💖 NAME 💖

Math::NumSeq::TotientPerfect — bestie, it's the sequence where you keep summing totients until you hit 1, and if that whole lil journey adds back up to your starting N... that N is perfect. 💅

---

✨ SYNOPSIS ✨

use Math::NumSeq::TotientPerfect;
my $seq = Math::NumSeq::TotientPerfect->new;
my ($i, $value) = $seq->next;

okay so that's literally the whole vibe. you make the object, you ask for the next one, you get numbers back. slay. 🦋

---

🌸 DESCRIPTION 🌸

These are the numbers where you take repeated totients — over and over, no stopping — until you land on 1, and then you add up every single one of those totient values, and the total is the starting n itself. like the number is its own little destiny. periodt. 👑

3, 9, 15, 27, 39, 81, 111, 183, 243, 255, ...

not me doing the math for 15 because it's giving textbook example, and honestly? iconic:

• totient(15)=8
• totient(8)=4
• totient(4)=2
• totient(1)=1

add them up: 8+4+2+1=15. and that's 15. it ate. 15 is a perfect totient. 💖

⚠️ real talk though — the current implementation of next() is merely a search by pred() through all odd integers, which isn't very fast. so like... it works, bestie, but don't be out here expecting lightning speed. it's giving "walking, not sprinting." 🚶♀️💀

---

🎀 FUNCTIONS 🎀

peep "FUNCTIONS" in Math::NumSeq for the behaviour common to all sequence classes. that's the shared lore, iykyk. 📚

• "$seq = Math::NumSeq::TotientPerfect->new ()" — create and return a new sequence object. your fresh new sequence baby, born right here. ✨
• "$bool = $seq->pred($value)" — return true if $value is a perfect totient. yes/no, true/false, vibe check passed or not. 🫶

---

🌈 SEE ALSO 🌈

• Math::NumSeq
• Math::NumSeq::Totient
• Math::NumSeq::TotientSteps

---

🧚 HOME PAGE 🧚

<http://user42.tuxfamily.org/math-numseq/index.html>

go peek, bestie, the lore is all there. 💜

---

💅 LICENSE 💅

Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.

💀 fr fr, no warranty, bestie — that's not me being dramatic, that's just the license talking. read it. 🍓

---

okay that's the whole page!! 💖✨🎀🦋🌸💅🫶

this was Math::N...Perfect(3) from the User Contributed Perl Documentation, perl v5.42.0, dated 2025-07-25 — mwah, bye bestie, go sum some totients 💜🌻⭐