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A133205
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Fully multiplicative with a(p) = p*(p+1)/2 for prime p.
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0
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1, 3, 6, 9, 15, 18, 28, 27, 36, 45, 66, 54, 91, 84, 90, 81, 153, 108, 190, 135, 168, 198, 276, 162, 225, 273, 216, 252, 435, 270, 496, 243, 396, 459, 420, 324, 703, 570, 546, 405, 861, 504, 946, 594, 540, 828, 1128, 486, 784, 675, 918, 819, 1431, 648, 990, 756
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OFFSET
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1,2
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COMMENTS
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There are analogues with the triangular numbers replaced by some other sequence, but this was chosen because of the parity coincidences of A034953.
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LINKS
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Table of n, a(n) for n=1..56.
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FORMULA
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a((p_1)^e_1)*(p_2)^e_2)*...*(p_k)^e_k)) = (T((p_1))^e_1)*T((p_2))^e_2)*...*T((p_k))^e_k, where T(i) = A000217(i). a(p_i) = A034953(i).
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PROG
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(PARI) a(n)=my(f=factor(n)); prod(i=1, #f[, 1], binomial(f[i, 1]+1, 2)^f[i, 2]) /* Charles R Greathouse IV, Sep 09 2010 */
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CROSSREFS
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Cf. A000040, A000217, A003958, A003959, A003960, A003961, A003964, A034953.
Sequence in context: A179893 A133331 A000741 * A049991 A143981 A031940
Adjacent sequences: A133202 A133203 A133204 * A133206 A133207 A133208
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KEYWORD
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mult,easy,nonn
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AUTHOR
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Jonathan Vos Post, Oct 10 2007
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STATUS
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approved
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