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 A323243 a(1) = 0; for n > 1, a(n) = A000203(A156552(n)). 77
 0, 1, 3, 4, 7, 6, 15, 8, 12, 13, 31, 12, 63, 18, 18, 24, 127, 14, 255, 20, 39, 48, 511, 24, 28, 84, 24, 48, 1023, 32, 2047, 32, 54, 176, 42, 40, 4095, 258, 144, 56, 8191, 38, 16383, 68, 36, 800, 32767, 48, 60, 31, 252, 132, 65535, 30, 91, 72, 528, 1302, 131071, 44, 262143, 2736, 60, 104, 126, 96, 524287, 304, 774, 42, 1048575, 72, 2097151, 4356, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552) FORMULA a(1) = 0; for n > 1, a(n) = A000203(A156552(n)). a(n) = 2*A156552(n) - A323244(n). a(n) = A323247(n) - A323248(n). From Antti Karttunen, Mar 12 2019: (Start) a(A000040(n)) = A000225(n). a(n) = Sum_{d|n} A324543(d). For n > 1, a(2*A246277(n)) = A324118(n). gcd(a(n), A156552(n)) = A324396(n). A000035(a(n)) = A324823(n). (End) MATHEMATICA Array[If[# == 0, 0, DivisorSigma[1, #]] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]] &, 75] (* Michael De Vlieger, Apr 21 2019 *) PROG (PARI) A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)}; A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n)))); A323243(n) = if(1==n, 0, sigma(A156552(n))); (PARI) \\ For computing terms a(n), with n > ~4000 use Hans Havermann's factorization file https://oeis.org/A156552/a156552.txt v156552sigs = readvec("a156552.txt"); \\ First read it in as a PARI-vector. 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))); \\ Then play sigma \\ Antti Karttunen, Mar 15 2019 CROSSREFS Cf. A000203, A156552, A323244, A323247, A323248, A324118, A324543 (Möbius transform), A324396, A324823. Cf. A323173, A324054, A324184, A324545 for other permutations of sigma, and also A324573, A324653. Sequence in context: A053480 A258052 A241448 * A244974 A077580 A069213 Adjacent sequences:  A323240 A323241 A323242 * A323244 A323245 A323246 KEYWORD nonn AUTHOR Antti Karttunen, Jan 10 2019 STATUS approved

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Last modified December 10 23:29 EST 2019. Contains 329910 sequences. (Running on oeis4.)