A352797 Let S(k) be the subsequence of multiples of k from k*positive integers where each element of S(k) sets a new record of divisors in that sequence. Then f(k) is the first element from S(k)/k that is not a power of 2. Sequence lists records for f(k).
1, 3, 9, 45, 135, 945, 2835, 14175, 155925, 467775, 6081075
Offset: 1
Examples
For k=1, the sequence of multiples of 1 that set records for numbers of divisors (divided by 1) starts 1,2,4,6. (A002182) For k=3, the sequence starts 1,2,4,8,12. (A351623) For k=9, the sequence starts 1,2,4,8,16,20. For k=45, the sequence starts 1,2,4,8,16,24.
Programs
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PARI
isp2(n) = if (n<=2, return(1)); my(m); ispower(n,,&m) && (m==2); f(n) = {my(m=1, nm, k=1, ok=0); until(ok, nm = numdiv(k*n); if (nm > m, m = nm; if (!isp2(k), ok = 1);); if (!ok, k++);); k;} lista(nn) = {my(m=1, fm); for (n=1, nn, fm = f(n); if (fm > m, m = fm; print1(n, ", ");););} \\ Michel Marcus, May 05 2022
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