A377878 Numbers k for which A276085(k) is a multiple of 3125, where A276085 is fully additive with a(p) = p#/p.

1, 4823, 8267, 9553, 15623, 15833, 15929, 20633, 23393, 28417, 33079, 34027, 36941, 37129, 37939, 42599, 43249, 44431, 47291, 49374, 60097, 65832, 66323, 69287, 69749, 70613, 74063, 74281, 74333, 74999, 77231, 83881, 86191, 86551, 87776, 88727, 99683, 106481, 108673, 111366, 113922, 115729, 118517, 124841, 126054, 129337

Offset: 1

Author

Antti Karttunen, Nov 13 2024

Keywords

• nonn

Comments

A multiplicative semigroup; if m and n are in the sequence then so is m*n.

Question: Does this sequence have asymptotic density? See also questions in A377872 and A377869.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..15711
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000720, A276085, A377869, A377877.

Subsequence of A373140, and of A377873.

Cf. also A377872.

Programs

PARI

isA377878(n) = { my(m=5^5, f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= Mod(prime(i),m); i++); s += f[k, 2]*pr); (0==lift(s)); };

Formula

{k such that Sum e*A377877(A000720(p)-1) == 0 (mod 5^5), when k = Product(p^e)}.