cp's OEIS Frontend

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

%I A352844 #42 May 31 2022 02:05:05
%S A352844 2,3,8,5,15,7,21,25,35,11,33,13,39,117,65,17,51,19,57,121,95,23,69,
%T A352844 169,115,483,161,29,87,31,93,279,155,651,217,37,111,333,185,41,123,43,
%U A352844 129,387,215,47,141,423,235,954,318,53,159,477,265,841,354,59,177,61
%N A352844 Smallest k > 1 such that sopfr(k) - tau(k) = n, or -1 if no such k exists.
%C A352844 Conjecture: There is no -1 in this sequence.
%H A352844 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 A352844 It appears that the sequence satisfies these rules, for large m:
%F A352844 Rule 1: a(prime(m+1) - 2) = prime(m+1)
%F A352844 Rule 2: a(prime(m+1) - 1) = 3*prime(m+1)
%F A352844 Rule 3: a(prime(m+1) + 1) = 5*prime(m+1)
%F A352844 Rule 4: a(prime(m+1) - 3) = 6*prime(m+1)
%F A352844 Rule 5: a(prime(m+1) + 3) = 7*prime(m+1)
%F A352844 Rule 6: a(prime(m+1)) = 9*prime(m+1)
%F A352844 Rule 7: a(prime(m+1) - 7) = 11*prime(m+1)
%F A352844 Rule 8: a(prime(m+1) + 7) = 12*prime(m+1)
%F A352844 Rule 9: a(prime(m+1) + 9) = 13*prime(m+1)
%F A352844 ...
%F A352844 Choose the first rule that applies.
%o A352844 (PARI) f(m) = my(fp=factor(m)); sum(k=1, #fp~, fp[k,1]*fp[k,2]) - numdiv(fp);
%o A352844 a(n) = my(k=2); while(f(k) != n, k++); k; \\ _Michel Marcus_, Apr 06 2022
%Y A352844 Cf. A000005, A001414.
%K A352844 nonn
%O A352844 0,1
%A A352844 _Nicolas Bělohoubek_, Apr 05 2022