

A086333


Index power of 2 in the first highly composite number m such that omega(m)=n.


1



1, 1, 2, 3, 3, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 9, 9, 9, 9, 10, 10, 10, 10, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 10, 10, 10, 10
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OFFSET

1,3


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..4095
A. Flammenkamp, First 1200 highly composite numbers


FORMULA

a(n) = A007814(A086332(n)).  David Wasserman, Mar 21 2005


PROG

(PARI) count = 0; v = vector(2000000); pp = vector(90); pp[6] = 1; for (i = 7, 90, pp[i] = prime(i)*pp[i  1]); for (a = 0, 14, n2 = 2^a; for (b = 0, min(a, 8), n3 = n2*3^b; for (c = 0, min(b, 5), n5 = n3*5^c; for (d = 0, min(c, 4), n7 = n5*7^d; for (e = 0, min(d, 3), n11 = n7*11^e; for (f = 0, min(e, 3), n13 = n11*13^f; if (f > 1, for (g = 6, 12, npp2 = n13*pp[g]; for (h = g, 90, n = npp2*pp[h]; count++; v[count] = n)), if (f == 1, for (h = 6, 100, n = n13*pp[h]; count++; v[count] = n), count++; v[count] = n13)))))))); v = vecsort(v); dmax = 0; omax = 0; for (i = 1, count, dn = numdiv(v[i]); if (dn > dmax, dmax = dn; o = omega(v[i]); if (o > omax, omax = o; f = factor(v[i]); print(f[1, 2])))); (Wasserman)


CROSSREFS

Cf. A002182, A001221, A007814, A086332.
Sequence in context: A029107 A209727 A063123 * A240792 A217121 A253783
Adjacent sequences: A086330 A086331 A086332 * A086334 A086335 A086336


KEYWORD

nonn


AUTHOR

Lekraj Beedassy, Sep 01 2003


EXTENSIONS

More terms from David Wasserman, Mar 21 2005


STATUS

approved



