OFFSET

1,1

COMMENTS

Friends m and n are primitive friendly iff they have no common prime factor of the same multiplicity.

There may be other primitive friendly integers within the range of those given, but they have yet to be calculated.

All perfect numbers are 2-primitive-friendly (since they are all products of distinct powers of 2 and distinct Mersenne primes). - Daniel Forgues, Jun 24 2009

A friendly integer can be both primitive and nonprimitive. For example, consider 30. First, 30 is friendly to 140, but this relation is nonprimitive, because it is 5 times the friendly pair {6, 28}. But then, 30 is also friendly to 6200, and this is a primitive pair (not a scaling of a smaller friendly pair). - Jeppe Stig Nielsen, Dec 07 2022

LINKS

Claude W. Anderson and Dean Hickerson, Problem 6020: Friendly Integers, Amer. Math. Monthly 84 (1977) pp. 65-66.

Dean Hickerson, Friendly number, post to newsgroup sci.math, Jan 31, 2000.

Walter Nissen, Primitive Friendly Integers and Exclusive Multiples, 2004 post to NMBRTHRY mailing list.

EXAMPLE

While 6 and 28 are not coprime because they share the common factor 2, the factor 2 appears twice in 28 but only once in 6, so they are in the sequence.

From Suyash Pandit, Oct 15 2023: (Start)

280 is primitive friendly with 1553357978368 = 2^8*7^2*19^2*37*73*127;

360 is primitive friendly with 155086041146982400 = 2^20*5^2*7^3*13*31*127*337;

380 is primitive friendly with 31701183232 = 2^8*19^2*37*73*127;

408 is primitive friendly with 874453888 = 2^7*7*11*17^2*307. (End)

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Walter Nissen, Jul 01 2004

EXTENSIONS

Offset 1 from Michel Marcus, Dec 13 2022

Terms 280, 360, 380, and 408 from Suyash Pandit, Sep 16 2023

STATUS

approved