A369646 Numbers k such that the difference A051903(k) - A328114(A003415(k)) reaches a new maximum in range 1..k, where A051903 is the maximal exponent in the prime factorization of n, A328114 is the maximal digit in the primorial base expansion of n, and A003415 is the arithmetic derivative.

1, 8, 16, 832, 1024, 95232, 131072, 2097152, 1006632960, 1090519040

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Index entries for sequences related to primorial base

Example

           k   factorization    max.exp.  k' in primorial  max digit  diff
                                                  base
           1                        0,              0,        0,       0
           8 = 2^3,                 3,            200,        2,       1
          16 = 2^4,                 4,           1010,        1,       3
         832 = 2^6 * 13^1,          6,         111120,        2,       4
        1024 = 2^10,               10,         222310,        3,       7
       95232 = 2^10 * 3^1 * 31^1,  10,       10021220,        2,       8
      131072 = 2^17,               17,       23132010,        3,      14
     2097152 = 2^21,               21,      252354100,        5,      16
  1006632960 = 2^26 * 3^1 * 5^1,   26,    23194866010,        9,      17
  1090519040 = 2^24 * 5^1 * 13^1,  24,    22053155300,        5,      19.
Here k' stands for the arithmetic derivative of k, A003415(k). Primorial base expansion is obtained with A049345.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
A351097(n) = (A328114(A003415(n))-A051903(n));
m=A351097(1); print1(1, ", "); for(n=2, oo, x=A351097(n); if(x<m, print1(n, ", "); m=x));

Crossrefs

Positions of records for -A351097(n).

After the initial 1, a subsequence of A351098.

Cf. A002110, A003415, A049345, A051903, A328114.

Cf. also A369645, A369647.

Sequence in context: A265094 A285060 A371009 * A061747 A109585 A284438

Adjacent sequences: A369643 A369644 A369645 * A369647 A369648 A369649

Keyword

nonn,more

Author

Antti Karttunen, Feb 02 2024

Status

approved