login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A172246 Consider all ways of writing n = a + b where a<=b, gcd(a,b,n)=1, and having the same value of the function N(a,b,n) defined as product of the distinct prime divisors of a*b*n. Let w be the list of frequencies of distinct terms N(a, b, n) found among these partitions. If no frequency is more than 1 then a(n) = 0, otherwise a(n) = [the sum of elements of w] - [the number of elements of w] + 1. 4
0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 3, 0, 2, 0, 4, 0, 3, 0, 0, 0, 2, 0, 4, 0, 0, 0, 3, 0, 3, 0, 2, 2, 3, 0, 3, 0, 0, 0, 5, 0, 4, 0, 0, 0, 4, 0, 4, 0, 2, 2, 3, 0, 5, 0, 2, 0, 4, 0, 4, 0, 0, 0, 7, 0, 7, 0, 0, 0, 5, 0, 6, 0, 0, 0, 4, 0, 3, 0, 0, 0, 5, 0, 5, 0, 3, 0, 4, 0, 5, 0, 3, 0, 5, 0, 6, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,6
LINKS
EXAMPLE
a(7)=2 because we have two partitions 7=1+6 and 7=3+4 with different values of N(a,b,n) respectively 1*2*3*7=42 and 2*3*7=42.
From David A. Corneth, Aug 25 2020: (Start)
a(23) = 4 as the terms occurring more than once (so omitting those that occur just once) listed with repetitions is (690, 690, 690, 966, 966) and so the list of frequencies is (3, 2) as 690 occurs thrice and 966 occurs twice.
As at least one of these multiplicities is larger than 1, a(n) = [sum of numbers in (3, 2)] - [number of numbers in (3, 2)] + 1 = (3 + 2) - 2 + 1 = 4. (End)
PROG
(PARI) a(n) = {l = List(); m = Map(); my(res = 0); for(i = 1, n\2, if(gcd([i, (n-i), n]) == 1, c = factorback(factor(i*(n-i)*n)[, 1]); listput(l, c); if(mapisdefined(m, c), mapput(m, c, mapget(m, c) + 1); , mapput(m, c, 1) ) ) ); l = Set(l); for(i = 1, #l, if(mapget(m, l[i]) > 1, res+=mapget(m, l[i]); ) ); w = vector(#l, i, mapget(m, l[i])); w = select(x -> x > 1, w); if(#w == 0, return(0)); w = vecsort(Vec(w)); return(vecsum(w) - #w + 1); } \\ David A. Corneth, Aug 25 2020
CROSSREFS
Sequence in context: A337346 A294902 A321516 * A087893 A079169 A345060
KEYWORD
nonn,less
AUTHOR
Artur Jasinski, Jan 29 2010
EXTENSIONS
Edited by David A. Corneth, Aug 25 2020, and N. J. A. Sloane, Sep 05 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)