A180460 a(n) is the smallest number m such that sigma(m)=22^n, or 0 if m does not exist.

1, 0, 0, 10363, 136647, 3018141, 66411009, 1636922343, 31276995183, 688217286267, 15200749439001, 324029599659171, 7264291502741679, 160447401116572437, 3530475812620849113, 75514126111770824037, 1662716417771040164631, 36586320846189859358019, 804905851136700392012493, 17704604426749226872106319

Offset: 0

Author

Walter Kehowski, Sep 06 2010

Keywords

• nonn

Comments

Conjecture: Given any even integer E not a power of 2 (see A078426) there exists a positive integer N such that for all n>=N the equation sigma(m)=E^n has at least one solution for m.

Examples

			a(4)=136647=3^4*7*241 since sigma(3^4*7*241)=(11^2)(2^3)(2*11^2)=2^4*11^4 and 136647 is the smallest such number.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A048251, A110077, A180265, A180461, A180462, A180463, A180464.

Extensions

Terms a(37) onward (in b-file) from Max Alekseyev, Mar 04 2014