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 A190665 Numbers n such that sum of aliquot parts of n is a nontrivial power: sigma(n) - n = a^b  for integers a>1, b>1. 0
 9, 10, 12, 15, 24, 26, 49, 56, 58, 69, 75, 76, 90, 95, 119, 122, 124, 133, 140, 143, 147, 153, 176, 194, 215, 243, 287, 332, 363, 386, 407, 429, 477, 495, 507, 511, 524, 527, 536, 551, 568, 575, 578, 688, 717, 738, 791, 794, 815, 867, 871, 892, 924, 935, 961, 963, 992, 1001, 1018, 1075, 1083, 1159, 1196, 1199, 1243, 1295, 1304, 1324, 1346, 1391, 1415, 1421, 1431, 1532, 1573, 1587 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Similar to A065496. LINKS EXAMPLE 122: aliquot parts: 1, 2, 61, sum: 1+2+61 = 64 = 8^2 140: sum of aliquot parts: 1+2+4+5+7+10+14+20+28+35+70 = 196 = 14^2. MAPLE isA001597 := proc(n) for a from 2 do if a^2 > n then return false; end if; for b from 2 do if a^b =n then return true; elif a^b>n then break; end if; end do; end do: end proc: isA190665 := proc(n) isA001597(numtheory[sigma](n)-n) ; end proc: for n from 1 to 2000 do if isA190665(n) then printf("%d, ", n) ; end if; end do; # R. J. Mathar, May 30 2011 PROG (PARI) ypower(n)= { local(f, p=0); f=factor(n); if(gcd(f[, 2])>1, p=1); return(p) } {  for (n=1, 1000, a=sigma(n)-n; if(ypower(a), print1(n, " "))) } /* Antonio Roldán, Oct 23 2012 */ CROSSREFS Cf. A065496, A001597, A048699. Sequence in context: A181698 A342146 A048592 * A242475 A160947 A158581 Adjacent sequences:  A190662 A190663 A190664 * A190666 A190667 A190668 KEYWORD nonn AUTHOR Antonio Roldán, May 16 2011 STATUS approved

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Last modified June 23 13:01 EDT 2021. Contains 345401 sequences. (Running on oeis4.)