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

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..9.

Example

           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.

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]));
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, ", "))));

Crossrefs

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

Cf. also A351073, A369642, A369646, A369649.

Sequence in context: A032136 A032040 A045661 * A078707 A085332 A204424

Adjacent sequences: A369644 A369645 A369646 * A369648 A369649 A369650

Keyword

nonn,hard,more

Author

Antti Karttunen, Feb 02 2024

Status

approved