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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.
2
1, 8, 16, 832, 1024, 95232, 131072, 2097152, 1006632960, 1090519040
OFFSET
1,2
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); };
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. also A369645, A369647.
Sequence in context: A265094 A285060 A371009 * A061747 A109585 A284438
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Feb 02 2024
STATUS
approved