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

2, 5, 9, 15, 25, 36, 52, 73, 98, 129, 167, 213, 270, 338, 421, 517, 632, 768, 920, 1102, 1311, 1547, 1824, 2143, 2501, 2911, 3379, 3906, 4493, 5164, 5920, 6757, 7704, 8765, 9943, 11247, 12706, 14324, 16103, 18078, 20268, 22666, 25315, 28239, 31437, 34941, 38785, 43002

Offset

1,1

Comments

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) ).

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..108

Mathematica

mx = 10^108; lst = Sort@ Flatten@ Table[
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,
{a, 0, Log[ 2, mx], 2},
{b, 0, Log[ 3, mx/ 2^a], 3},
{c, 0, Log[ 5, mx/(2^a*3^b)], 5},
{d, 0, Log[ 7, mx/(2^a*3^b*5^c)], 7},
{e, 0, Log[11, mx/(2^a*3^b*5^c*7^d)], 11},
{f, 0, Log[13, mx/(2^a*3^b*5^c*7^d*11^e)], 13},
{g, 0, Log[17, mx/(2^a*3^b*5^c*7^d*11^e*13^f)], 17},
{h, 0, Log[19, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g)], 19},
{i, 0, Log[23, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h)], 23},
{j, 0, Log[29, mx/(2^a*3^b*5^c*7^d*11^e*13^f*17^g*19^h*23^i)], 29},
{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},
{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},
{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},
{n, 0, Log[43, 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},
{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},
{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},
{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}]

Crossrefs

Cf. A072873.

Sequence in context: A134342 A100287 A007176 * A176691 A339554 A274355

Adjacent sequences: A267754 A267755 A267756 * A267758 A267759 A267760

Keyword

nonn

Author

Robert G. Wilson v, Jan 20 2016

Status

approved