A351097 - OEIS

A351097

Difference between {the maximal digit value in primorial base expansion of the arithmetic derivative of n} and {the maximal exponent in the prime factorization of n}.

0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 2, 1, 1, 0, -1, 0, 1, 1, -1, 0, 0, 0, -2, 1, 2, 1, 0, 0, 2, 1, -1, 0, 1, 0, 1, -1, 3, 0, -1, 0, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 3, 3, 0, 2, 0, 0, 2, 1, 2, 1, 0, 1, -1, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 1, 1, 2, 3, -3, 0, 0, 0, 2, 0, 2, 0, 2, 1

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OFFSET

1,16

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..30030

FORMULA

a(n) = A328390(n) - A051903(n) = A051903(A327859(n)) - A051903(n).

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]));

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };