A324200 a(n) = 2^(A000043(n)-1) * ((2^A059305(n)) - 1), where A059305 gives the prime index of the n-th Mersenne prime, while A000043 gives its exponent.

6, 60, 32752, 137438953408

Offset: 1

Author

Antti Karttunen, Feb 18 2019

Keywords

• nonn

Comments

If there are no odd perfect numbers then these are the positions of zeros in A324185.

The next term has 314 digits:

11781361728633673532894774498354952494238773929196300355071513798753168641589311119865182769801300280680127783231251635087526446289021607771691249214388576215221396663491984443067742263787264024212477244347842938066577043117995647400274369612403653814737339068225047641453182709824206687753689912418253153056583680.

Crossrefs

Subsequence of A023758 and A324199.

Cf. A000043, A000396, A000668, A000720, A007814, A023758, A059305, A156552, A243071, A324185.

Programs

PARI

A324200(n) = (2^(A000043(n)-1))*((2^primepi(A000668(n)))-1);

Formula

a(n) = ((2^A000720(A000668(n)))-1) * 2^(A000043(n)-1) = ((2^A059305(n)) - 1) * 2^(A000043(n)-1).

a(n) = A243071(A156552(A324201(n))) = A243071(A156552(A062457(A000043(n)))).

If no odd perfect numbers exist, then a(n) = A243071(A000396(n)), and thus A007814(a(n)) = A007814(A000396(n)).