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The C and Perl code in this repository provides a variety of resources aimed at finding values of OEIS sequences such as A292580, the values $D(n,k)$ representing the smallest chain of exactly $k$ consecutive integers that each have $n$ divisors. I.e. $D(n,k)=mind:\mathrm{\forall }i:0<=i<k⟹\tau (d+i)=n$. (Note that in the sequence page it refers to $T(n,k)=D(2n,k)$, since when $n$ is odd only $D(n,1)$ exists.)

The Perl code (which also includes some inline C) searches for values of this sequence and several similar sequences of arithmetic progressions ("AP") of numbers sharing divisor-related characteristics. Most of the Perl programs accept a "type" option (-y<type>) that specifies which sequence type to consider:

• option -yo, module Type::OneSeq, $mind:\mathrm{\forall }i:0<=i<k⟹\tau (d+i)=n$
• • C executable pcoul
• option -yt, module Type::TauSeq, $mind:\mathrm{\forall }i:0<=i<k⟹\tau (n+id)=\tau (n)$
• option -ya, module Type::AddSeq, $mind:\mathrm{\forall }i:0<=i<k⟹\tau (d+in)=n$
• • C executable pcaul
• option -yr, module Type::Track, $mind:\mathrm{\forall }i:0<=i<k⟹\tau (n+i)=\tau (d+i),d\ne n$
• • C executable pcrul
• option -ys, module Type::Semip, $mind:\mathrm{\forall }i:0<=i<k⟹d+in$ is a semiprime (of the form $pq$ or $p^2$)
• option -yd, module Type::AscDPrime, AP with minimum start point, fixed difference, $i$th element has $i$ distinct prime factors
• option -yn, module Type::AscNPrime, AP with minimum start point, fixed difference, $i$th element has $i$ prime factors with multiplicity