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A267757 Number of terms of A072873 less than or equal to 10^n. 1

%I

%S 2,5,9,15,25,36,52,73,98,129,167,213,270,338,421,517,632,768,920,1102,

%T 1311,1547,1824,2143,2501,2911,3379,3906,4493,5164,5920,6757,7704,

%U 8765,9943,11247,12706,14324,16103,18078,20268,22666,25315,28239,31437,34941,38785,43002

%N Number of terms of A072873 less than or equal to 10^n.

%C A072873: Numbers n such that sum( e(i)/p(i) ) is an integer, where the prime factorization of n is Product( p(i)^e(i) ).

%H Robert G. Wilson v, <a href="/A267757/b267757.txt">Table of n, a(n) for n = 1..108</a>

%t mx = 10^108; lst = Sort@ Flatten@ Table[

%t 2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j*31^k*37^l*41^m*43^n*47^o*53^p,

%t {a, 0, Log[ 2, mx],2},

%t {b, 0, Log[ 3, mx/ 2^a], 3},

%t {c, 0, Log[ 5, mx/(2^a*3^b)], 5},

%t {d, 0, Log[ 7, mx/(2^a*3^b*5^c)], 7},

%t {e, 0, Log[11, mx/(2^a*3^b*5^c*7^d)], 11},

%t {f, 0, Log[13, mx/(2^a*3^b*5^c*7^d*11^e)], 13},

%t {g, 0, Log[17, mx/(2^a*3^b*5^c*7^d*11^e*13^f)], 17},

%t {h, 0, Log[19, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g)], 19},

%t {i, 0, Log[23, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h)], 23},

%t {j, 0, Log[29, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i)], 29},

%t {k, 0, Log[31, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j)], 31},

%t {l, 0, Log[37, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j*31^k)], 37},

%t {m, 0, Log[41, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j*31^k*37^l)], 41},

%t {n, 0, Log[43, mx/

%t 2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j*31^k*37^l*41^m)], 43},

%t {o, 0, Log[47, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j*31^k*37^l*41^m*43^n)], 47},

%t {p, 0, Log[53, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j*31^k*37^l*41^m*43^n*47^o)], 53},

%t {q, 0, Log[59, mx/ 2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i*29^j*31^k*37^l*41^m*43^n*47^o*53^p)], 59}]; Table[ Length@ Select[lst, # <= 10^n &], {n, 108}]

%Y Cf. A072873.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jan 20 2016

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Last modified July 2 01:17 EDT 2022. Contains 354984 sequences. (Running on oeis4.)