A336918 Numbers k such that A000005(k) divides A003973(k); numbers k for which A336839(k) = 1.

1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 101

Offset: 1

Author

Antti Karttunen, Aug 12 2020

Keywords

• nonn

Comments

Numbers k such that A003961(k) is in A003601. Numbers which become (or stay as) arithmetic numbers when all primes in their prime factorization are replaced by the next larger primes.

Numbers k for which A003973(k) is equal to A000005(k)*A336838(k).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Wikipedia, Arithmetic number
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A003601, A003961, A003973, A336838, A336930.

Positions of ones in A336839.

Cf. A336919 (complement).

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA336918(n) = !(sigma(A003961(n))%numdiv(n));