A080613 Minimal sequence such that Omega(a(m))<=Omega(a(n)) for m<n, where Omega=A001222 (sum of exponents in prime factorization).

1, 2, 3, 4, 25, 6, 49, 8, 27, 20, 1331, 12, 2197, 28, 45, 16, 83521, 36, 130321, 40, 189, 88, 279841, 24, 625, 104, 81, 56, 707281, 60, 923521, 32, 891, 272, 4375, 72, 69343957, 304, 1053, 80, 115856201, 168, 147008443, 176, 405, 368, 229345007, 48

Offset

1,2

Comments

a(n)=n iff n=2^k or n=3*2^k (A029744); A001222(a(n))=A000523(n).

Links

Table of n, a(n) for n=1..48.

Formula

a(1) = 1, a(n) = if Omega(n)<Omega(a(n-1)) then n*spf(n)^(Omega(a(n-1))-Omega(n)) else n, where spf=A020639 (smallest prime factor).

Crossrefs

Sequence in context: A000336 A287433 A235041 * A055006 A139050 A043309

Adjacent sequences: A080610 A080611 A080612 * A080614 A080615 A080616

Keyword

nonn

Author

Reinhard Zumkeller, Feb 25 2003

Status

approved