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A133205 Fully multiplicative with a(p) = p*(p+1)/2 for prime p. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There are analogs with the triangular numbers replaced by some other sequence, but this was chosen because of the parity coincidences of A034953.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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).

PROG

(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 */

CROSSREFS

Cf. A000040, A000217, A003958, A003959, A003960, A003961, A003964, A034953.

Sequence in context: A276381 A259728 A000741 * A049991 A143981 A031940

Adjacent sequences:  A133202 A133203 A133204 * A133206 A133207 A133208

KEYWORD

mult,easy,nonn

AUTHOR

Jonathan Vos Post, Oct 10 2007

STATUS

approved

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Last modified August 4 06:07 EDT 2020. Contains 336201 sequences. (Running on oeis4.)