A369649 -id:A369649 - cp's OEIS frontend

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

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

Offset: 1

Antti Karttunen, Feb 02 2024

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

			           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.

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

Cf. also A351073, A369642, A369646, A369649.

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,", "))));

A369648 Indices of novel terms in A351073, where A351073 is the maximal exponent in the prime factorization of the numbers that are sums of distinct primorial numbers.

Original entry on oeis.org

1, 2, 6, 7, 10, 24, 90, 144, 766, 1040, 1164, 2122, 3010, 8914, 17838, 20500, 87472, 243252, 312058, 1118346, 1347998, 2167146, 3569780, 6038946

Offset: 1

Antti Karttunen, Feb 03 2024

Indices k at which A351073(k) for the first time attains a new distinct value.

			See examples in A369649.

Cf. A002110, A051903, A276156, A351073, A369649 (corresponding values of A276156).

Cf. also A369647.

A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A276156(n) = { my(s=0, p=1, r=1); while(n, if(n%2, s += r); n>>=1; p = nextprime(1+p); r *= p); (s); };
A351073(n) = A051903(A276156(n));
m=Map(); for(n=1,2^25,e=A351073(n);if(!mapisdefined(m,e),mapput(m,e,n);print1(n,", ")));

cp's OEIS Frontend

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

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