A348950 a(n) = A348507(A276086(n)), where A348507(n) = A003959(n) - n, A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.

0, 1, 1, 6, 7, 30, 1, 8, 9, 42, 51, 198, 11, 58, 69, 282, 351, 1278, 91, 398, 489, 1842, 2331, 8118, 671, 2638, 3309, 11802, 15111, 50958, 1, 10, 11, 54, 65, 258, 13, 74, 87, 366, 453, 1674, 113, 514, 627, 2406, 3033, 10674, 853, 3434, 4287, 15486, 19773, 67194, 5993, 22354, 28347, 98166, 126513, 418914, 15, 94, 109

Offset: 0

Author

Antti Karttunen, Nov 06 2021

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003959, A276086, A348507, A348949, A348999.

Cf. also A327860.

Programs

PARI

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A348507(n) = (A003959(n) - n);
A348950(n) = A348507(A276086(n));

PARI

A348950(n) = { my(m1=1, m2=1, p=2); while(n, m1 *= (p^(n%p)); m2 *= ((1+p)^(n%p)); n = n\p; p = nextprime(1+p)); (m2-m1); };

Formula

a(n) = A348949(n) - A276086(n) = A348507(A276086(n)).