A351256 Maximal exponent in the prime factorization of A351255(n).

0, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 3, 4, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6

Offset: 1

Author

Antti Karttunen, Feb 11 2022

Keywords

• nonn

Comments

The largest digit in the primorial base representation of A328116(n).

The scatter plot gives some sense of how it is harder to eventually reach zero by iterating A003415, when starting from a number with large exponent(s) in its prime factorization. See also A099308.

Examples

			A328116(27) = 50, and A049345(50) = "1310", where the largest primorial base digit is 3, therefore a(27) = 3. Equally, A351255(27) = 2625 = 3 * 5^3 * 7, thus A051903(2625) = 3 and a(27) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..105368 (computed for all 19-smooth terms of A351255, and also for A276086(9699690) = 23)

Crossrefs

Cf. A003415, A049345, A051903, A099308, A276086, A328114, A328116, A351255, A351257, A351258.

Programs

PARI

A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i,2]>=f[i,1],return(0), s += f[i, 2]/f[i, 1])); (n*s));
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); };
A099307(n) = { my(s=1); while(n>1, n = A003415checked(n); s++); if(n,s,0); };
for(n=0, 2^9, u=A276086(n); c = A099307(u); if(c>0,print1(A051903(u), ", ")));

Formula

a(n) = A328114(A328116(n)) = A051903(A351255(n)).

For all n, a(n) < A351257(n). [See A351258 for the differences].