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4, 9, 12, 20, 44, 52, 60, 108, 124, 125, 132, 140, 156, 172, 188, 204, 236, 300, 308, 396, 412, 436, 476, 492, 612, 644, 700, 836, 876, 884, 891, 924, 972, 980, 1004, 1044, 1092, 1100, 1116, 1148, 1188, 1196, 1236, 1260, 1268, 1292, 1300, 1308, 1372, 1380, 1476, 1620, 1628, 1724, 1860, 1900, 2140, 2244, 2324, 2356, 2444, 2460, 2652, 2660, 2700
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OFFSET
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1,1
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COMMENTS
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Notably, of the first 150 terms (4 .. 9996), 156 = 2^2 * 3 * 13 is the only even term that does not map to a prime, as A156552(156) = 267 = 3*89 (and sigma(267) = 360 = 4*90).
Although sigma(A156552(k)) = A323243(k) is a multiple of 4 for most of the terms k present in this sequence, there are exceptions, for example 840350 = A005940(1+A332445(1)) = 2^1 * 5^2 * 7^5 is one, as A048675(A332223(840350)) = 98 = 2*A048675(840350) and A323243(840350) = 2394 == 2 (mod 4).
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LINKS
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PROG
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(PARI)
\\ To find all terms < 10000:
v156552sigs = readvec("a156552.txt"); \\ Use the factorization file for A156552 prepared by Hans Havermann, available at https://oeis.org/A156552/a156552.txt
A323243(n) = if(n<=2, n-1, my(prsig=v156552sigs[n], ps=prsig[1], es=prsig[2]); prod(i=1, #ps, ((ps[i]^(1+es[i]))-1)/(ps[i]-1)));
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
for(n=2, 10000, if(isA322225(n), print1(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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