A370114 Numbers k for which A276086(A003415(k)) is a multiple of k, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

1, 2, 6, 10, 15, 42, 50, 70, 98, 105, 245, 294, 330, 343, 375, 726, 770, 825, 1029, 1078, 1155, 1210, 1375, 1617, 1694, 1815, 1925, 2310, 2450, 2541, 2662, 2695, 3025, 3822, 3850, 4290, 4550, 4719, 5005, 5145, 5390, 6125, 6655, 7098, 7150, 7546, 7865, 8450, 8470, 8575, 8918, 9317, 9438, 9555, 10010, 11319, 11375

Offset: 1

Author

Antti Karttunen, Feb 11 2024

Keywords

• nonn

Comments

Numbers k that divide A327859(k). Sequence contains only terms of A048103 and does not contain any multiples of 9.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..7501

Crossrefs

Fixed points of A369964. Positions of 1's in A370116.

Intersection of A048103 and A369650 is a subsequence of this sequence. See the comments in latter.

Cf. A003415, A276086, A327859, A370115.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA370114(n) = ((n>0) && !(A276086(A003415(n))%n));