A369647 Nonzero numbers k in A341518 for which A051903(k) attains novel values.

1, 2, 9, 16, 108, 9024, 2990880, 995336192, 1805726080

Offset: 1

Author

Antti Karttunen, Feb 02 2024

Keywords

• nonn
• hard
• more

Comments

Indices of record values of A051903 attained for the terms of A341518 is a subsequence: 1, 2, 9, 16, 9024, 995336192.

Examples

			           k   factorization           max.exp         k'    A049345(k')
           1                              0,           0,            0
           2 = 2^1,                       1,           1,            1
           9 = 3^2,                       2,           6,          100
          16 = 2^4,                       4,          32,         1010
         108 = 2^2 * 3^3,                 3,         216,        10100
        9024 = 2^6 * 3 * 47,              6,       30272,      1011010
     2990880 = 2^5 * 3^2 * 5 * 31 * 67,   5,    10210416,    110010100
   995336192 = 2^13 * 121501,            13,  6469693440,  10000010000
  1805726080 = 2^7 * 5 * 157 * 17971,     7,  6692788416,  11000100100.
See also the examples at A351073 and A369649.
		

Crossrefs

Cf. A003415, A049345, A051903, A276086, A327859, A328114, A341518.

Cf. also A351073, A369642, A369646, A369649.

Programs

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]));
ismaxprimobasedigit_at_most(n,k) = { my(s=0, p=2); while(n, if((n%p)>k, return(0)); n = n\p; p = nextprime(1+p)); (1); };
isA341518(n) = ismaxprimobasedigit_at_most(A003415(n),1);
m=Map(); for(n=1,2990880,if(isA341518(n),e=A051903(n);if(!mapisdefined(m,e),mapput(m,e,n);print1(n,", "))));