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

Author

Antti Karttunen, Jan 31 2024

Keywords

• nonn

Comments

See comments in A024451.

Links

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

Crossrefs

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

Cf. also A368702.

Programs

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)));

Formula

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