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 A180162 a(n) is the smallest number N such that sigma(N) is an n-th power but not a higher power, with a(n) = 0 if no such number exists. 5
 1, 2, 3, 7, 510, 21, 17490, 93, 217, 381, 651, 118879530, 2667, 8191, 11811, 24573, 57337, 82677, 172011, 393213, 761763, 1572861, 2752491, 5332341, 11010027, 21845397, 48758691, 85327221, 199753347, 341310837, 677207307, 1398273429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Ray Chandler, Table of n, a(n) for n=1..469 FORMULA a(n) >= A063869(n). [From R. J. Mathar, Aug 20 2010] EXAMPLE a(4)=510 since 510=2*3*5*17, sigma(510)=2^4*3^4. a(11)=2*3*5*7*11*53*971=118879530 since sigma(118879530)=6^11. MAPLE with(numtheory); egcd:=proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z-> z[2], L); igcd(op(L)) else 0 fi end: P:={}: SP:={}: for w to 1 do for n from 1 to 12^6 do sn:=sigma(n); esn:=egcd(sn); if not esn in P then P:=P union {esn}; SP:=SP union {[esn, n]}; printf("n=%d, esn=%d, sn=...\n", n, esn); print(ifactor(sn)); fi; od; #n od; #w P; SP; CROSSREFS Cf. A065496, A000203, A175432, A169981. Sequence in context: A100763 A132538 A062615 * A129907 A046284 A069503 Adjacent sequences:  A180159 A180160 A180161 * A180163 A180164 A180165 KEYWORD nonn AUTHOR Walter Kehowski, Aug 14 2010, Aug 19 2010 EXTENSIONS a(11) found by Walter Kehowski and Artur Jasinski, Aug 16 2010 Edited by N. J. A. Sloane, Aug 19 2010 a(23) onwards from Ray Chandler, Aug 19 2010 STATUS approved

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