On
The Big Bang Theory's episode "The Athenaeum Allocation", Sheldon mentions to Amy that for their proposed wedding date, May 12,
"The month squared equals the square of the sum of the members of the set of the prime factors of the day. Isn't that romantic?"
Amy's reply contorts a Shakespeare quote: "shall I compare thee to a day that's also a really weird math problem?"
It's indeed weird as the squaring is introduced for no reason at all.
But also, how rare is the circumstance? What other dates of the year exhibit the property? Remember that because of the setmembership criterion, each prime factor is included in the sum only once: 12 has prime factors 2 and 3, and those add up to 5, for May.
I'm not considering here number 1 (as in the problem) and the number itself when it is a prime number (it's not clear for me from what is in the text) as prime divisors: we can forget the days of the month with prime numbers. Also January, is out of consideration with this rule.
Feb: 4,8,16
March:9,27
May:6,12,18,24
July:10,20
August:15
September:14,28
October:21,25,30
seventeen days
plus days without month: 22,26, two days
plus prime days, 1,2,3,5,7,11,13,17,19,23,29,31 twelve days
Total 31 days.
If we decide to include prime numbers:
1,2,3,5,7,11 should be added to their respective months.
Edited on March 12, 2018, 11:20 am
Il post di J. shows an error in post. 25 is on May not on October
Edited on March 12, 2018, 4:06 pm

Posted by armando
on 20180312 11:14:39 