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 A139306 Ultraperfect numbers: 2^(2p - 1), where p is A000043(n). 24
 8, 32, 512, 8192, 33554432, 8589934592, 137438953472, 2305843009213693952, 2658455991569831745807614120560689152, 191561942608236107294793378393788647952342390272950272 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sum of n-th even perfect number and n-th even superperfect number. Also, sum of n-th perfect number and n-th superperfect number, if there are no odd perfect and odd superperfect numbers, then the n-th perfect number is the difference between a(n) and the n-th superperfect number (see A135652, A135653, A135654 and A135655). LINKS FORMULA a(n) = 2^(2*A000043(n) - 1). Also, a(n) = 2^A133033(n), if there are no odd perfect numbers. Also, a(n) = A000396(n) + A019279(n), if there are no odd perfect and odd superperfect numbers. Also, a(n) = A000396(n) + A061652(n), if there are no odd perfect numbers, the we can write: perfect number A000396(n) = a(n) - A061652(n). a(n) = A061652(n)*(A000668(n)+1) = A061652(n)*A072868(n). - Omar E. Pol, Apr 13 2008 EXAMPLE a(5)=33554432 because A000043(5)=13 and 2^(2*13 - 1) = 2^25 = 33554432. Also, if there are no odd perfect and odd superperfect numbers then we can write a(5) = A000396(5) + A019279(5) = A000396(5) + A061652(5) = 33554432. CROSSREFS Cf. A000079, A000396, A019279, A061645, A061652, A133033, A135652, A135653, A135654, A135655, A139286, A139294, A139307. Cf. A000043, A000668, A072868. Sequence in context: A120781 A288454 A139286 * A214594 A288457 A166995 Adjacent sequences:  A139303 A139304 A139305 * A139307 A139308 A139309 KEYWORD nonn AUTHOR Omar E. Pol, Apr 13 2008 STATUS approved

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)