

A342013


Position of the nth colossally abundant number in A329886, the primorial inflation of Doudnatree.


5



1, 2, 5, 9, 19, 21, 37, 75, 139, 267, 535, 539, 555, 1067, 2091, 4139, 8279, 16471, 32855, 32919, 32923, 65691, 131227, 262299, 524599, 1048887, 2097463, 4194615, 4194647, 8388951, 16777559, 33554775, 67109207, 67109463, 134218327, 268436655, 536872111, 536872119, 1073743031, 2147484855, 2147485879, 4294969527, 8589936823
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OFFSET

1,2


COMMENTS

Like A342012, also this sequence is monotonic. Proof: the doubling step corresponds here to step *2 + 1, and "bumping up" some of the prime factors likewise results a larger A156552code, thus both steps keep the result growing.
The binary length of these numbers (A070939, = 1+A000523) grows by 0 or 1 at each step, thus the next colossally abundant number is always found on either on the same row (right of the current CAnumber), or the next row of A329886, the row immediately below. The next CAnumber will be on the same row only when its factorization contains neither a new prime nor yet another instance of prime 2.


LINKS



FORMULA



PROG

(PARI)
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1])  1); res += (p * p2 * (2^(f[i, 2])  1)); p2 <<= f[i, 2]); res};


CROSSREFS

Cf. A004490, A005940, A073751, A108951, A156552, A319626, A329886, A329900, A342000, A342010 (the binary weight), A342011, A342012.


KEYWORD

nonn


AUTHOR



STATUS

approved



