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!)
A352844 Smallest k > 1 such that sopfr(k) - tau(k) = n, or -1 if no such k exists. 1

%I #42 May 31 2022 02:05:05

%S 2,3,8,5,15,7,21,25,35,11,33,13,39,117,65,17,51,19,57,121,95,23,69,

%T 169,115,483,161,29,87,31,93,279,155,651,217,37,111,333,185,41,123,43,

%U 129,387,215,47,141,423,235,954,318,53,159,477,265,841,354,59,177,61

%N Smallest k > 1 such that sopfr(k) - tau(k) = n, or -1 if no such k exists.

%C Conjecture: There is no -1 in this sequence.

%H Alois P. Heinz, <a href="/A352844/b352844.txt">Table of n, a(n) for n = 0..10000</a> (first 516 terms from Nicolas Bělohoubek)

%F It appears that the sequence satisfies these rules, for large m:

%F Rule 1: a(prime(m+1) - 2) = prime(m+1)

%F Rule 2: a(prime(m+1) - 1) = 3*prime(m+1)

%F Rule 3: a(prime(m+1) + 1) = 5*prime(m+1)

%F Rule 4: a(prime(m+1) - 3) = 6*prime(m+1)

%F Rule 5: a(prime(m+1) + 3) = 7*prime(m+1)

%F Rule 6: a(prime(m+1)) = 9*prime(m+1)

%F Rule 7: a(prime(m+1) - 7) = 11*prime(m+1)

%F Rule 8: a(prime(m+1) + 7) = 12*prime(m+1)

%F Rule 9: a(prime(m+1) + 9) = 13*prime(m+1)

%F ...

%F Choose the first rule that applies.

%o (PARI) f(m) = my(fp=factor(m)); sum(k=1, #fp~, fp[k,1]*fp[k,2]) - numdiv(fp);

%o a(n) = my(k=2); while(f(k) != n, k++); k; \\ _Michel Marcus_, Apr 06 2022

%Y Cf. A000005, A001414.

%K nonn

%O 0,1

%A _Nicolas Bělohoubek_, Apr 05 2022

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 August 8 15:25 EDT 2024. Contains 375022 sequences. (Running on oeis4.)