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A337045
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Indecomposable sigma-powerful numbers: powerful numbers k such that sigma(k) is also powerful, but restricted to terms that are not the product of 2 terms > 1 of A337044.
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4
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81, 343, 400, 9261, 189728, 224939, 972000, 1705636, 2205472, 3087000, 3591200, 3648100, 7968032, 13645088, 15350724, 21161304, 24240600, 25992000, 26680500, 29184800, 32832900, 48586824, 51595489, 80802000, 103617387, 109215352, 110215125, 119604096, 122805792
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OFFSET
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1,1
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COMMENTS
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This is an implementation of the suggestion that Walter A. Kehowski made on his website (see link) with regard to so-called indecomposable sigma-powerful numbers. However, the results deviate from the table linked there. The table is considered to be deficient.
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LINKS
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EXAMPLE
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No two proper divisors of 400 are sigma-powerful and have the product of those divisors 400 so 400 is in the sequence.
27783 = 81 * 343 is sigma-powerful but 81 and 343 are sigma-powerful as well so 27783 can be decomposed into two sigma-powerful factors. So 27783 is not in the sequence. (End)
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PROG
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(PARI) v=vector(50); n=0;
for(m=2, 150000000, my(is); if(ispowerful(m) && ispowerful(sigma(m)), v[n++]=m; is=1; for(j=1, n-1, if(v[n]%v[j], , if(vecsearch(v[1..n-1], v[n]/v[j]), is=0; break))); if(is, print1(v[n], ", "))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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