A369647 - OEIS

A369647

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

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

(list; graph; refs; listen; history; text; internal format)

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

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

KEYWORD

nonn,hard,more

AUTHOR

STATUS

approved