A369651 The second arithmetic derivative of primorial numbers.

0, 0, 1, 1, 32, 1, 1, 37712, 381596, 9835475, 36880858, 5221912091, 149759057759, 186024798, 456607833524310, 655374897748042, 32188411533060, 3002590335363139484, 1, 1, 1489192548103758778136571, 905624730150525686386253700, 1, 110832638787270947169636975150, 331748330219014906068858, 349669183443106226663011852002384

Offset

0,5

Comments

See comments in A024451.

Links

Antti Karttunen, Table of n, a(n) for n = 0..49

Formula

a(n) = A003415(A024451(n)) = A068346(A002110(n)).

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369651(n) = A003415(A003415(A002110(n)));

Crossrefs

Cf. A002110, A003415, A024451, A068346, A109628 (positions of 1's).

Cf. also A368702.

Sequence in context: A354946 A351000 A174923 * A351809 A176341 A134203

Adjacent sequences: A369648 A369649 A369650 * A369652 A369653 A369654

Keyword

nonn

Author

Antti Karttunen, Jan 31 2024

Status

approved