A180265
a(n) = smallest k such that sigma(k) = 14^n, or zero if no such k exists.
Original entry on oeis.org
1, 13, 0, 1164, 15132, 230484, 2823492, 36705396, 508541124, 7194470556, 100696385244, 1503091145388, 19540184890044, 273550891167372, 3811871194625676, 53378900339114532, 727176010568075796, 10177815744800162004, 142523339476298463228, 1994910930816765350844, 27918212600229725023068
Offset: 0
a(0)=1 since sigma(1)=14^0=1. a(1)=13 since sigma(13)=14. a(2)=0 since no N exists such that sigma(N)=14^2. a(6)=2823492=2^2*3*7*33613 since sigma(2823492)=14^6 is the first 6th power. a(7)=36705396=2^2*3*7*13*33613 since sigma(36705396)=14^7 is the first 7th power.
A180460
a(n) is the smallest number m such that sigma(m)=22^n, or 0 if m does not exist.
Original entry on oeis.org
1, 0, 0, 10363, 136647, 3018141, 66411009, 1636922343, 31276995183, 688217286267, 15200749439001, 324029599659171, 7264291502741679, 160447401116572437, 3530475812620849113, 75514126111770824037, 1662716417771040164631, 36586320846189859358019, 804905851136700392012493, 17704604426749226872106319
Offset: 0
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.
A180462
a(n) is the smallest number m such that sigma(m)=34^n, or 0 if m does not exist.
Original entry on oeis.org
1, 0, 0, 38659, 1333447, 45356239, 1542131167, 52432478719, 0, 44114690056791, 1545604624685757, 52550557239372861, 1542390446782691499, 52463299805385993363, 1783774217997898256739, 60648345436543315211523, 2091915317967934350057159, 69957029735592536691912261
Offset: 0
a(3)=38659=67*577 since sigma(67*577)=(2^2*17)*(2*17^2)=2^3*17^3 and 38659 is the smallest such number.
A180463
a(n) is the smallest number m such that sigma(m)=38^n, or 0 if m does not exist.
Original entry on oeis.org
1, 37, 0, 0, 0, 0, 0, 85811686941, 3175032416817, 159809964979789, 4561513295803851, 155532888827892597, 5754716886632026089, 249887680992407652771, 8319571903089894983277, 307824160414326114381249, 12077787753685017948512649, 455818072892233197941369463
Offset: 0
a(7)=85811686941=3*28603895647 since sigma(85811686941)= (2^2)*(2^5*19^7)=2^7*19^7 and 85811686941 is the smallest such number.
A180464
a(n) is the smallest number m such that sigma(m)=46^n, or 0 if m does not exist.
Original entry on oeis.org
1, 0, 0, 0, 0, 180217597, 6217507317, 325975026477, 15034820907837, 919684211139697, 31808042757482763, 1463508270300620883, 58746435953696315769, 2709539295335742607689, 138000408890542031957601, 5718143312090439006662949, 263735727094699893912217269
Offset: 0
a(5)=180217597=7*25745371 and sigma(180217597)=(2^3)*(2^2*23^5)=2^5*23^5 and 180217597 is the smallest such number.
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